Of all the delightfully improbable scenarios depicted in Bill & Ted's Excellent Adventure – from Napoleon Bonaparte causing havoc on a waterslide to Billy the Kid and Socrates (aka "So-crayts", of course) picking up chicks in a California mall to George Carlin acting in a film alongside Keanu Reeves and a member of the Go-Go's – none would have seemed more unlikely on its release than the idea that one day, with much media fanfare, the public would be celebrating the film's 25th anniversary.

By the time Bill & Ted was released in 1989, the 80s teen film explosion was starting to taper out. Heathers, which came out in 1987, had so deftly satirised the conventions of the genre (and particularly of John Hughes's films) that teen films were losing their Hughesian innocence and becoming instead laden with self-conscious irony, leading to the 90s trend of remaking classic literature with teenagers (Clueless, 10 Things I Hate About You, She's All That).

Moreover, there had already been plenty of films about time-travelling teens by the time Bill & Ted rocked up in cinemas, such as Peggy Sue Got Married and Back to the Future. Few who were around then would have bet that a goofy movie about a pair of California metalheads skipping back through time in a phonebox collecting historical characters to bring back to 20th-century California for their history report would still be remembered today. But I am very much among those few.

For reasons I can't remember now, I didn't see Bill & Ted at the cinema. I first came across it the following year when my mother rented it for me after I announced to her, at the age of 12, that I was deeply in love with Keanu Reeves and so would probably marry him (it was the early 90s, when it was the law for every heterosexual female under 35 to be in love with Reeves.) My mother was extremely supportive of my new relationship (my father, on the other hand, never quite mastered the pronunciation of my fiance's first name) so when I informed her that a mere rental was an insufficient token of my new relationship, she bought the video for me for the commitment-sealing sum of £9.99. My little sister and I duly watched that tape to ribbons.

What I didn't tell my mother, however, was that my love for the film was not simply about Reeves. In fact, after one viewing I had also developed a crush on his co-star, Alex Winter, with his goofy looks, his almost camp California accent, his keen deployment of the single raised eyebrow and, most of all, his intriguing cropped top. But there was more going on here than mere pre-pubescent lust (although there was quite a lot of that).

One of the reasons it's so unlikely Bill & Ted is celebrating its 25th anniversary is because the film very nearly didn't come out at all. DeLaurentiis Entertainment Group originally produced it, but nearly shelved it when the company ran in to financial problems.

"I hate to say it, but we kind of gave up on the movie," Winter recalls on the phone from LA. "It was much closer to the chopping block than anyone knows."

Eventually, a small video company called Nelson Entertainment bought the film for peanuts and made – to the astonishment of everyone involved – an absolute fortune out of it. The movie went on to spawn a sequel (Bill & Ted's Bogus Journey), a cartoon and even a breakfast cereal ("It was disgusting, hahaha!" Winter hoots.)

Another factor that nearly scuppered the movie was that Reeves and Winter weren't really meant to be cast. Ed Solomon and Chris Matheson, who wrote the script, envisaged Bill S Preston Esquire and Ted Theodore Logan as "14-year-old skinny guys, with low-rider bellbottoms and heavy metal T-shirts", Solomon said in a 1991 interview. "We actually had a scene that was even shot with Bill and Ted walking past a group of popular kids who hate them. But once you cast Alex and Keanu, who look like pretty cool guys, that was hard to believe." Yet the casting directors were wise in their choice, because by 1989 those of us who had grown up watching teen films were getting sick of nerds. We'd already had a sci-fi teen film starring two dweebs, Weird Science; it was lame at the time and has not aged well since. We were ready for beautiful boys. And by "we", I mean "I".

It's hard to convey just how ubiquitous Bill & Ted's California dude-talk became after the film was released. Winter and Reeves were even asked on TV to explain the precise meaning of the word "bodacious" ("outstandingly outstanding", apparently). Does Winter feel any responsibility for all those kids annoying the hell out of their parents with terms like "gnarly" and "Yes way"?

"Yes. Without a doubt. I remember once I was in Paris between the first and the second Bill & Ted films and there were all these French kids talking like Bill and Ted and I thought, holy crap, what have we done?"

Winter had already been in one huge 80s teen film before Bill & Ted: while studying film at New York University, he was cast in 1987's The Lost Boys, in which he was part of Kiefer Sutherland's vampire crew. "That was incredibly fun, one of the real happy times of my youth. It was the first time I was on the set of a big studio Hollywood film, and [the director] Joel Schumacher and [cinematographer] Mike Chapman were there. I mean, Chapman shot Raging Bull – hello? For an NYU film student it was basically like hanging round God," he says.

But the reaction to Bill & Ted was an entirely new experience. "The day it came out I remember walking into a restaurant and everyone in there freaked out when they saw me – I'd never had anything like that before," he says. "And my life's never been the same. There hasn't been a day since then that someone hasn't come up to me to ask about Bill & Ted."

Considering how much Winter has had to talk about Bill & Ted over the past quarter-century, he is adorably enthused on the subject. I was a little wary about interviewing him, partly because I worried my inner 12-year-old would blurt out a question about whether he still wears his cropped top (and the inner 12-year-old does just that in the first minute of our conversation, to which Winter good-naturedly replies, "I think I'd look like the dad from Family Guy if I did that"), but also because I feared he might be a film snob and therefore snooty about the mighty Bill & Ted. I'd read an interview in which he, heretically, said Bill & Ted "is not exactly Citizen Kane or Star Wars", which is obviously true, as Bill & Ted is a billion times more fun than either of those po-faced films. Right, Alex?

"Hahaha! I don't mean to be disparaging about Bill & Ted, I'm really proud of it. But what I meant was, it's not on Sight and Sound's list of greatest movies of all time," he reassures me.

Well, it should be.

"Yeah, maybe it should," he agrees, correctly.

The reasons why it should are multiple, but let's start with the most obvious: it's really funny and, even more unusually, it's funniness has held up well. Winter and Reeves are both charismatic enough for their gagging ("Who's Joan of Arc?" "Noah's wife!") and mugging ("Whoa!") to still be endearing and amusing as opposed to cheesy and cringeworthy (see the previously mentioned Weird Science for examples of the latter.) They bring such puppyish energy to the roles that not even Reeves, dozens of roles later, has ever really escaped from the film's shadow, or the general assumption that he was basically playing himself. Winter, meanwhile, has become a respected director based in London, New York and LA. Doesn't it bother him that his public persona is that of a Californian airhead?

"No, not at all. I'm a pretty private person, so it's kind of useful that my public persona is so different from my own persona. It kind of gives me cover – it's a good deflection shield," he says.

The other actors and characters contribute to the film, too, of course. Particularly George Carlin as Rufus, the guide from the future, who brings dry wit to the silliness.

"Ahh, George, he was so great," says Winter fondly (Carlin died in 2008). "Initially they were thinking of casting action people, actors like Sean Connery in the role. I was so happy when they decided to go for a comedian, and George said yes right away. Rufus is pretty gentle and understated and that's exactly how George was off camera, very different from his comedy persona. He really was a very sincere, big-hearted, understated guy."

Terry Camilleri as Napoleon is especially funny ("Mon Dieu!"), cheating at bowling and terrorising Californian children. Joan of Arc is played by Winona Ryder lookalike Jane Wiedlin. While she doesn't get much to do in the film, she should be singled out for being not just a member of the Go-Go's, but the singer of one of the best 80s pop songs, Rush Hour.

"Oh God, I can tell you now that I had the BIGGEST crush on her when I was in high school. I went to see the Go-Go's play and I just stood over by her side of the stage and stared at her for two hours. I think I still did that while we were shooting – just stood off to the side and stared at her like an idiot," says Winter.

Bill & Ted isn't trying to coin a universal teen experience, like John Hughes's films did, but nor is it trying to be ironic. It just wants to be fun, and it is. But the film really works because it has such sweetness to it, and this comes from the friendship at its heart – Winter and Reeves have been best pals ever since.

"He's like my brother – we hang out all the time together. We go on holidays together and our families are very close. He is one of my very, very closest friends," Winter says.

People must go crazy when they see you guys together, I say. "We get some pretty fun reactions. The film really captures two friends going through something crazy together, and that's what it was like for Reeves and me in the wake of the film. I don't think you can fake something like that."

Do you always call him Reeves?

"Oh yeah, always. I'm not even sure if I can remember how to pronounce his first name. It's like something you ride around in on a lake with a couple of paddles, right?" (My father would sympathise.)

There are always rumours about sequels being made of successful 80s films, most of which sound deeply misguided, from Ghostbusters 3 to Top Gun 2. But the long rumoured Bill & Ted 3, which looks like it might actually happen, is one I would happily go see. "It's Hollywood, so could the film all go down the tubes? Yes. But I believe we'll get it up and running," says Winter confidently.

After all, if the friendship between the two leads is still alive, then the film's heart still is, too. And that heart was always bodacious.

• Bill & Ted's Excellent Adventure anniversary blu-ray steelbook is available now. Alex Winter's film Downloaded is available at downloadedthemovie.com