Founded in October of 1998, Fanfiction.net has millions of users from across the globe, with stories in 40 languages in such fandoms as Star Wars, Pokemon, and Avatar: the Last Airbender. The stories in question are divided into multiple categories–Anime/Manga, Books, Cartoons, Comics, Games, Movies, TV Shows, and Miscellaneous–then organized further by the specific fandom (ex. the Yu-Gi-Oh subsection can be found under Anime/Manga), each having a separate section for crossovers.
The site is free to join, allowing users to submit stories, maintain a user profile, act as a beta reader, communicate via private messages, maintain a list of favorite stories and authors, and leave comments. However, there are limits to what can be posted–stories with explicit material, reader-insertion fics, songfics (stories that have songs with copyrighted lyrics), and fan fics based on certain copyrighted works are not allowed.
Archive of Our Own
Another popular place to find fan fiction is Archive of Our Own, or AO3 for short. Launched in November of 2009, AO3 uses a tag system and permits readers to leave ‘kudos’, similar to the ‘likes’/’hearts’ system on sites like Twitter and Tumblr. In addition, unlike Fanfiction.net, AO3 permits explicit material and things like reader-insertion fics–although it does ask for content warnings for things like ‘Major Character Death’ and ‘Graphic Depictions of Violence’–as long as the material is legal.