Platoon isn't like Harry Potter, with a huge, ginormous, massive fan club apparatus. It's a very sobering and bloody war film, and those kinds of things don't usually make people want to don costumes and reenact scenes. With that said, there is plenty of Internet buzz about the film, even three decades later. The film definitely made a splash, and really reminded the people of the U.S. about all the bad stuff that went down in Vietnam.
Like lots of movies, Platoon does have its own wiki, complete with character bios and other assorted factoids. Aside from a few scattered oddities, such as this trio of dolls based on the film's three main characters there's not much out there.
Most of the fan-atical energy out there is dedicated to the individual actors and, of course, to director Oliver Stone. If you want to check out what some of the avid Stone-ites have to say, check out this site. If you want more, try this one.
For Charlie Sheen, you've got a ton of options. There's this Official Fan Club, sure, but also other assorted sites like this and this. For Johnny Depp, you can go here.
While some of the film's less flashy, but still great actors, stars (Tom Berenger, John C. McGinley, Willem Dafoe) don't have super cool sites devoted to them, you can still find scattered discussions and aborted fanpop pages if you really look hard.