Harry Potter Fan Fiction
Harry Potter FanFiction is thought of as one of the more commonly known parts of the fandom. Even people who wouldn't go to a convention and don't listen to Wizard Rock often write and read Harry Potter FanFiction. There are several ships (short for relationships), and sometimes people love their pairing so much it sparks conflict. There are several kinds of pairings for example Slash, Het, Threesomes, and even some more eccentric ones that would best be classified as Treestiality or Beastiality. There are many interesting pairings. Fanfics range anywhere from G to NC-17. There are also many "eras" in Harry Potter FanFiction. These eras are not just set during Harry's time at Hogwarts; other extremely popular eras are Marauder Era and Next Gen. There are several universes of FanFics, they aren't just Wizard. Some of them make the main wizard characters muggles. One other thing that makes Harry Potter FanFiction different from other series is that the author (J.K. Rowling) has approved of people writing Harry Potter FanFics. She not only approves but encourages it, unlike other authors.
While most Fan Fiction is of a narrative form, some works take the form of plays. Some of these are Musical Theater productions and can range from parody (such as A Very Potter Musical by Team Starkid, to the very much canon based The Final Battle by Lena Gabrielle (The Butterbeer Experience.) Other works of parody (of a non-musical sort) include Sally Cotter and the Censored Stone by Dean O'Carroll.
 Web Sites
There are many different websites people use to read/write fanfiction. There are some websites that are exclusive to Harry Potter Fanfiction, and others that host many stories. Some other websites are used that aren't fanfic-specific like blogging and journal websites (eg LiveJournal).
The most commonly used website is Fanfiction.net under which you can look at Harry Potter fanfiction, crossovers, and other fandoms. Many users have created communities that make lists of stories pertaining to a certain theme (ex. Severus Snape, Time-turner, Ships, etc.) that users can subscribe to to check out new stories. Also users of the site can subscribe to stories in progress to get notifications when a new chapter is up. The search feature on the website itself is mediocre but google is easier where you can type a theme and the word Fanfiction and find communities (ex. Severus Snape Fanfiction Community). The site is free but if you would like to write your own stories, reviews, or join a community you will need an account.
Another website is Mugglenet's Fanfiction archive. Their website is generally lesser known but with a good browse you are sure to find something. The site is free and no registration is needed.