I am guilty of the sin of Fanfic, aka Fan Fiction, and you know what? It was a ton of fun. Having free reign over what goes on in a favourite universe you're a fan of is a liberating experience indeed. Yes, it can lead to extreme cases of wrongness and into the demented realms of slash fiction, but as long as it is kept clean and the characters stay as they are in their official stories, fanfic can be an entertaining thing to read an to write.
Mine? I wrote a six-part Doctor Who story that ended up running to around 10,000 words. It was posted on a Doctor Who messageboard (a year or so before the announcement of Doctor Who coming back to TV), and was a bit of fun, nothing more. A lot of people take their fanfic very seriously, with whole story arcs playing out over many episodes of their stories, or in the case of Doctor Who, entire seasons put together. These 'seasons' of fanfic stories are generally put together by several writers with a shared aim, and as mad as it may seem, they can actually be kinda cool.
Whatever you're into, there is a ton of fanfic you can enjoy/stare in horror at. The most notorious one in recent years is the trend for Harry Potter fanfiction, which has so many bizarre permutations that it boggles the mind. In fact, JK Rowling had some fanfiction taken down due to its questionable content, and not just the atrocious writing ;)
Seriously though if you can't get enough of Star wars, Star Trek, Spider-man, X-Men, Doctor Who, Torchwood, He-Man or whatever, there's someone out there writing fanfic that you'll be into. There are even rare occasions where fanfic has become someone's actual profession.
The best example of this is the publishing house FanDemonium, who publish official Stargate and Stargate Atlantis novels, licensed directly from Metro Goldwyn Mayer. The story behind those books is that Sally Malcolm, a huge Stargate fan who wrote loads of Stargate fanfiction, and her husband Tom, enquired at MGM as to who had the novel rights to put out new Stargate novels. Two days later, they got a message from MGM offering them the rights and asking for a business plan.
They faced the challenge head-on, despite being somewhat thrown in at the deep end! Enlisting friends and other talented writers, they set about putting out new Stargate novels that fans would love. That range is now one of the most consistently fan-pleasing tie-in novel ranges in print.
That's a rare occurrence though. fanfiction is generally only enjoyed b7y diehard fans of a particular character or universe, but the fact that the stories are unofficial and can't be sold (it is against the law to sell unlicensed stories set in established universes) frees the writes from having to hold back and think of budget and studio constraints. While these fanfiction stories won't get you anywhere financially, they are a superb way to express your love for your favourite film or TV series, and are also a great way to improve your writing skills. So have some fun with it, and think of the readers- what would other fans like to read?