It is early on a chilly November morning in New York, the day before Thanksgiving, and Tim Burton seems to have decided that being in motion is too ambitious for the frigid weather. He is staying in a sedate suite at a small hotel on the Upper East Side, and the plan to go for a walk and talk - without the pedometer - is reviewed. Dressed all in black, looking sleep-deprived and pale and sniffling with a cold, Burton digs his hand into his ungroomed nest of black hair and scratches his head. "What do you think?" he asks, wincing. "Maybe we should just stay here." Expectation swirls around Tim Burton, not just because of the film projects he favours but also because of his cultivated look - that he is weird, or nerdy, even. But within seconds of being in his presence it's clear: it's a label that means nothing other than he's different. He understands that there are people who see the world literally, and people - like himself - who challenge that. He doesn't distort who he is. He doesn't appear to be fragile or enigmatic at all. He's relaxed and accessible; friendly and voluble.

"I'm not a dark person," he says, amused. His sentences rarely get finished and he waves his arms and hands in the air as though conducting an invisible orchestra of thoughts. "That's the one that always gets me. So what if I wear dark clothing and like monster movies - that doesn't mean that I'm a dark person. I've always actually felt like a really light person. Emotional. I don't smile in photographs - so?"

It doesn't affect him - or make him upset - that there is this perception of him: it makes him laugh. "It says more about the people saying it than it says about me."

Burton's movies champion the absurd and celebrate the misfit, and he has built his reputation on imaginative visuals. Now he is the most inside outsider in Hollywood. He creates peculiar characters and makes surreal-minded and haunting films (Sleepy Hollow, Edward Scissorhands, Batman) but they are lyrical and touching too. There is always a sense of love trumping all cynicism. But perhaps what distinguishes him most is an appreciation of people who don't, or can't, fit in.

Not surprisingly, Burton prefers to make his home outside of Hollywood. He lives in north London on and off with his wife, the actress Helena Bonham-Carter, and their son, Billy. He moved there when working on Batman and felt strangely at home, in a country where many Americans mistake a sense of irony for cynicism.

"When you get down to the regular people, I find them to be great - not cynical at all. I didn't get any of that stuff that you hear about. Before I left, you hear, 'Oh, they don't like Americans,' but I never felt it. I've been trying to analyse a little bit why I like it so much. I like the international flavour - the mix of people. There's more acceptance of eccentric behaviour. Not that I consider myself eccentric, but I felt more at home. You see more eccentrics. Slightly different behaviour is more accepted. I'm terrified of socialising but I find when you go out, it's more interesting. They're more tied to the world."

Burton grew up in perpetually sunny Burbank, California - an antiseptic suburb of Los Angeles. His film Edward Scissorhands is a satire of that environment and the alienation it imposed on him. The outcast rejected by suburbia was palpable in the confined pain of Johnny Depp's character snipping away at the topiary.

"Growing up in LA, I felt I was in a weird bubble. Last time I went back, there was this perfect symbol of the life out there: the city was surrounded by [forest] fires, and I had to go to this Hollywood luncheon and I was just making small talk with someone and I mentioned the fires and he gives me this look: 'Fires? What fires?' And I mean, the sky outside is filled with smoke and it's been going on for days and I just thought, 'Well, that's the problem here, you know?'"

"Every time I go back to Los Angeles it seems like it gets brighter," he says, rubbing his eyes and letting out an anguished sigh. "I feel like a vampire. Like someone cranked up the light meter an extra 30%. And, uh, I don't know. I always felt isolated. But in London, where I don't even socialise that much, I feel like I'm more connected to something. That feeling was there every time I went and it's stayed with me."

Burton was married, briefly, in 1989 to a German painter but they broke up a few years later and he became engaged in 1992 to the actress-model Lisa Marie. They lived together, were constant companions and she was often described as his "muse". Whether or not that's true, he cast her in several of his movies (as sexy Vampira in Ed Wood, Ichabod Crane's voluptuous mother in Sleepy Hollow, a Martian in Mars Attacks!, a chimpanzee in Planet of the Apes) and they frequently discussed their bond in interviews. It was said they "inhabited the same planet".

Burton left that planet in 2001. He met his girlfriend, Helena Bonham-Carter, while directing her as a chimp in Planet of the Apes, and she gave birth last October to their son, Billy. Now, at 45, Burton had become a father for the first time. "I resisted being a father for a long time. I didn't have a close relationship with my parents and didn't think I was capable - or had the skills. But I feel great about it. No one prepares you for how strange it is. I was completely shocked and surprised. It was beautiful."

Whether it's in his earliest work, like Pee-wee's Big Adventure, his 1985 version of a surreal kids' TV show, or 1994's Ed Wood, a black-and-white biography of the most talentless director of all time, Burton's films are all shaped by the confidence of a dislocated outsider's perspective.

Hollywood favours childlike visionaries, and Burton's vision is full of wonder but it's strange and poetic too. He's all for subversion. He's childlike but not saccharine, and odd enough to be considered original, without going too far to be unpredictably alarming. Some critics have faulted him for this, saying his most recent film, Big Fish, is inventive but not daring.

Big Fish, based on the novel by Daniel Wallace, hovers between epic tall tales and touching family dynamics. When a son realises he's about to become a father, he also learns that his father, whom he never connected with, is running out of time. It covers familiar themes: alienation, what's real and what's fantasy, and how factual truth differs from emotional truth.

It's easy to assume that with this film, the death of his father and the paternal conflict are what really interested him.

"When that happened - and I wasn't close to him - it still affected me, and you just start thinking about the relationship and how odd and unique it is, and I was intrigued by it. It was hard to put into words, and I thought this script did a good job of symbolising the abstract struggles of things that are difficult to talk about."

Aside from the accessible sentiment of this movie, what sets it apart from other Burton films is that it has extensive dialogue, something he doesn't usually rely on. It's also a love story and a Homerian odyssey - all pieced together to make a narrative-driven adventure. So perhaps it's not just the paternal elements that attracted him.

"My reputation has been that I can never tell a story. People say, 'Well, the films look nice, but there's no story.' I have to say I disagree."

The movie stars Albert Finney as Edward Bloom, a man with a need to tell stories that people will remember and, in the process, construct his legacy. Ewan McGregor plays him as a young man who leaves his small southern town and embarks on a journey encountering giants and werewolves, conjoined Korean lounge sisters, and a big fish that refuses to be caught. Bloom's son, Will (played by Billy Crudup), is searching for the "real" truth - but a deeper level of truth emerges.

When it's mentioned that everyone I know who has seen it has cried, Burton acknowledges the emotional resonance. "It sneaks up on you. When I first saw it a week after shooting it - because I edit as we go along - I saw a rough cut and I got emotional and thought, 'Is it because I'm jet-lagged and I'm having a nervous breakdown from finishing, or whatever?' - so I couldn't tell if it was working in the proper way, but I was hopeful. It's an odd one. We all resist sentiment. I certainly resist it."

John August, the screenwriter for Big Fish, tells how Burton never bowed to studio pressure to make the main character more likable. "He believed that as long as the audience could understand what he was doing, they would like him."

Burton nods vigorously when asked if he has always trusted his vision. "It's all I had. There was a very specific moment in my life when I had a breakthrough. I was at the California Institute of Arts [Burton had a Disney fellowship] and we were in a drawing class, and I had been getting more and more exasperated because I was trying to fit into a certain style of drawing - the Disney way - and I almost had a breakdown, and I was just sitting there and I said, 'You know what? I can't draw like this. I'm just gonna draw whatever way I draw and that's it.' And at that moment, my drawings changed. In one second, I drew completely different. In a different style and a different way. It was like a drug experience - literally, my mind expanded."

He says as a child he'd always had confidence partly because he was a loner and very internal. He was drawn to Roald Dahl and Dr Seuss.

"I don't know why I was such a loner. It shows you how rigid society is, because I never felt strange and, until this day, I don't feel strange. I always felt like I was a normal person. I was quiet and I was not disruptive in school, and yet I was categorised. Why I was categorised as strange, I have no idea. But from the beginning, I was.

"I've always felt like somewhat of a quiet anarchist, but it helped my perceptive qualities because you're standing away from society looking at it. So I felt like a foreigner very early on."

He offers an example of something weird he's referring to, how his view of the world can be distorted by translation. "Okay, well, a journalist came here the other day and said [he slams his palm down on the table], 'Who are you? What are you all about?' I mean, I almost took him outside and picked a fight with him. You wouldn't believe it." His response? "I just laughed. I mean, how are you supposed to answer that?"

"But my favourite one, which I will never, ever, forget, is, many years ago - I think it was a German journalist - I was talking flippantly about growing up liking monster movies and being a fan of Vincent Price and how the guy really helped me in my life, and the journalist goes [thick German accent], 'Why? Were you in some sort of danger?'"

Burton was never close to his parents, and in the past four years both have died. His father, Bill, was a former baseball player and worked for the city's parks, while his mother, Jean, worked in a gift shop. He has a younger brother, Danny. When Burton was 12 he went to live with his grandmother, and he has said in the past that his grandmother told him that before he could walk he would try to crawl out of the house. Growing up in the suburbs, not relating to his parents, Burton reacted by doing the opposite of what was normal. "I always felt intelligent. I felt very old when I was young."

He saw things as a juxtaposition. What's normal was weird. What's weird was normal. "You feel like you're on the other side of the fence - all the time." But whereas some kids might get disheartened by that sort of alienation, Burton was bolstered by it.

Even his complicated estrangement with his mother didn't derail his internal acuity. "It was the classic Gaslight thing," he says, describing her, his voice rising in volume to illustrate his frustration. "She'd say, 'Be home at six o'clock.' So I'd make sure I was home at six. And then she'd say, 'I said be home at five o'clock.'"

"I remember getting to a point early on where I thought I was doing things I wasn't aware I was doing. I remember actually having a dream where I opened up a closet door and all my mother's lipsticks came tumbling down."

This unexpected recollection amuses him. "Very telling dream, perhaps? So, I had some psycho doubts there. But I always felt very comfortable about my fantasy life. It was private, so it was secure. I knew what was going on." He knew even then that hours spent drawing and watching monster movies were providing an escape - so he was, and still is, at ease in that world. Lacking cultural stimulation and variation from his upbringing propelled him to manufacture it for himself. Not having an interesting world to live in, he created one. Suddenly he slumps in his chair and weariness fills the room. Asked if it's because he's been doing a lot of press for the movie, he nods. "I hate it! You wish - not that it could be this way - but you wish they [movies]could do the talking for you. It's like I've never been a fan of artists talking about their paintings. The joy of seeing a painting is, it lets you make up your own mind."

That Burton feels that talking about the film somehow lessens it is telling. He is not driven by ego or desire for notoriety. He seems to want to make movies that wouldn't otherwise exist.

After high school, Burton began the Disney fellowship at the California Institute of Arts, and in 1979 he went to work for Disney as an animator. But drawing in the way Disney required was alien to him. "It felt like that show The Prisoner: it's all very nice - it's all very wonderful - and yet you're still kind of trapped."

He made his first five-minute short, Vincent, in 1982 - about the fantasies of a deeply depressed suburban boy, narrated by Vincent Price. It was a critical success. His next project was a short film called Frankenweenie. It was about a boy who brings his dead dog, Sparky, back to life. His first feature film was Pee-wee's Big Adventure, then he made Beetlejuice, then Batman in 1989 - a warped, disturbing take on the comic-book legend that ended up being a huge blockbuster. But Burton says there wasn't one moment in particular where he knew he'd "made it".

"I got lucky because I got to do a couple of short films, then Pee-wee's Big Adventure, and it did very well for what it was - but it was also on several of the worst-movies-of-the-year lists. It was the same with Beetlejuice. Which I always felt was very healthy. I know people who do their first movie and win an Academy Award and then they're in trouble for the rest of their lives. I've never had that kind of heady experience where it goes only one way.

He says that he learnt that every film is like the first. After doing three successful films for Warner Bros, they didn't want to let him do Edward Scissorhands and he had to take it elsewhere.

"They didn't get it. Whatever. Every film has been a struggle. Everybody else's perception is that if you have a success it's gonna get easier and you can do whatever you want. It's actually gotten more difficult with each film."

His success is not typical and the studios were concerned - they couldn't put their finger on why, exactly, the films were successful. They were also, he says, afraid "I might be a lunatic".

Does he ever go to the cinema to see his films? "I've often thought about that. But I have come to realise I just can't enjoy it. I feel very vulnerable. Very naked. Even if it's a positive experience. I feel very exposed or something. I don't know. I can't relax. I just can't sit there and, you know..." He twists his torso around in a gesture of looking back at an audience behind him and smugly smiles and sweeps his arm as though he's referring to the screen: "'I did a great job, didn't I?' I can't really do that. I know that's not what you're suggesting. I mean, I wish I had that a little bit, because those people are getting the most out of life. But that's not me, no." Instead, his enjoyment comes from other, less obvious forms of appreciation. For instance, someone told him that their dog really enjoyed watching The Nightmare Before Christmas. He loved that. And somebody brought him a bootleg Batman toy back from Mexico, where the caped crusader is in a dune buggy. He loved that too.

"Someone came up to me once and said, 'My child never speaks but he sings all the songs to The Nightmare Before Christmas.' Weird things like that, I find meaningful on some level. It's a response that makes you think deeper. Makes your mind go in a different direction and not down the plodding course." They represent the opposite of literalisation. "I'm fascinated by literal-minded people but it's not my vibe. It's not where I live. Every day you see things that are completely surreal. You turn on the news and feel like you're in some sort of parallel universe. It's weird. Look at it: you're watching a story about Iraq and then you see a crawl about Michael Jackson and then a box about the weather and you're going, 'Michael Jackson's fighting in Iraq? What's going on here?' It's too much overload and not enough surreal thought. Everyone is in the surreal thought, they're not thinking about it."

He mumbles something else about the news, technology and mobile phones. I stare at him. You don't have a mobile phone? He grins with mock indignation. "Yes I do!"

He explains that it's rarely on and he has never managed to finish a conversation on it. "No matter where I am, no matter what - it always goes out. Conversations always cut off. I've never actually said 'goodbye'. It's like my mobile and I have bad karma."

He's not an e-mail or computer person either. "I've never been a technoid. I like travelling by train. I have a romantic notion of having the time when you couldn't communicate at any given moment. Where there was silence and distance and you were alone and could think about things."

Having talked about literal people who know where they will be in a week, a month, a year, is there a source of consistency in his life - and if so, where does it come from? There is a long, long silence. "Uh..." Another 30-second pause. "Well, you can tell by the length of the dramatic pause that I've always had a real problem with that. I mean, we don't even know what we're going to be doing tomorrow for Thanksgiving yet." He pauses again. Thinking. "I doodle every day. 'Drawing' sounds a little too lofty. I doodle around every day. I also talk to Helena every day. I do things like that regularly - but it's not organised or anything."

The American Museum of the Moving Image in New York currently has an exhibition of his drawings that he has used as the basis for sets, costumes and make-up for most of his films - though he doesn't mention it.

Burton used to get depressed and went through a period where he took antidepressants. It was in between movies. However, he says the drugs were good because they made him even more depressed. He got so sick of being depressed, he eventually got over it. "I can use the argument that the chemicals worked - who knows? - but it actually felt more like a willpower thing for me. Enough, already." Still, he thinks that being happy and miserable is just part of life. He doesn't expect to be happy all the time. "It's a pressure. I always say: show me one person that's always happy. Or always just one thing. It wouldn't be a human being. It would be some sort of alien."

Two hours have passed. Burton jumps up - "Pardon me" - and strides out of the room. For a second I think the interview has abruptly ended. Then, from the bathroom, he calls out: "I'm getting some Kleenex."

He returns to the table with handfuls of tissues and sits down. "I've been talking for three days." He blows his nose. "I think it's made me sick."

It's clear that he's becoming distracted - ready to go downstairs and join Bonham-Carter and the baby. When I ask what they'll be doing the rest of the afternoon, he shrugs and responds: "Christmas shopping?" He feigns excitement at the prospect of doing something normal. But it's likely he'll find something surreal in the experience, which we can watch out for in his next project.