Fanfiction is fun stuff...it can be a parody or serious. But since it's just for practice writing and not for money no one cares... well the original author cares as well as the publisher because this fan fiction generates free publicity and excitement for upcoming new releases.
Original Star Trek series as well as Star Wars had a ton of it...in fact some of it got published and paid royalties.
Currently Harry Potter has the most fan fiction... Chronicles of Narnia has some too. A lot of Japanese Anime has a good bit too. Werewolves and Vampires rounding it out.
I'm trying to remember what else has a bunch of fanfiction going on...but I'm drawing a blank at the moment.
Japanese Anime,.. you mean like Naruto? *cough!* *cough!* (Literally the only Anime I watch, write and read fanfics for, and roleplay.)