When we say "fandoms," we usually think of guys dressed up as Captain Kirk, or regular meetings between book club folks who like to go delving into the work of their favorite authors. West Side Story doesn't quite fit into those vibes. Having said that, it's a phenomenally popular musical, and because it started out on stage, it appeals to people who dig plays more than movies. All of which gives it a very selective kind of fan base.
Broadway fans probably have the biggest claim on it, since it started out there. They love it in part because…well, because it's incredibly good, but also because it's a surprisingly downbeat and socially relevant story that arrived in an era when all you got from Broadway was shiny and happy. Its distinctiveness led to regular revivals in smaller theaters around the country: community theaters, high school theater clubs, anywhere that had an available stage and a copy of the lyrics. (Source)
For fans who just want to geek out to their favorite musical, there's sites like Fanpop and similar hangouts where they can get their Jet on. Facebook page? Check. Pinterest? Oh yeah. And if all else fails, you can usually just type in the name of a movie this big and come up with a heck of a fan site to indulge in.
Oh, and before we go, we should mention at least one big fan who's doing more than reminiscing. Steven Spielberg, who worked for decades to get the rights to the film, finally succeeded, and announced he'd be making a new version of the movie. We're always leery about rebooting a classic, but Big Steve has earned the benefit of the doubt and you can't say he's not a fan.