Fanfic is most excellent because it shows how people take ownership of a character and reinforce their own cultural values. In X-Files fanfic specifically, there are a slew of "MSR" stories -- that is "Mulder Scully Relationship" stories -- which allow the fans to deal with the "UST" ("Unresolved Sexual Tension") on the show.
There are also quite a lot of great conspiracy stories, Lone Gunmen Stories, Cancerman Stories which take the mythology and the smaller characters and give them more depth (or what the writer thinks their motives might be).
Fanfic is often times humorous -- one of my favorite stories is told from the point of view of Queequeg, Scully's (alligator-bait) Pomeranian, who was gobbled in an episode. You had to be there.
Some stories also take a very literary view of the X-Files, combining references authors like T.S. Elliot to William Shakespeare. I think that this reflects the thoughtful nature of the X-Files show -- whose creators have been known to put in references in their episodes to to Dostoevsky, Nabakov, and others.
Authors that I like: Nicole Perry, Cici Lean. Stories that I think are a "must read": The Magician Books (I, II, III), Perry's Road series, Angelis, and Hollow Men.
There are a couple of FUNNY AS ALL HELL "cross-overs" which I have read (stories that cross-over shows): Witness by Michele Martin (XF, Forever Knight, Quantum Leap, Starman, Highlander) and Julie Jekel's Top Secret (XF, Quantum Leap, Lois and Clark)
And how can I forget SLASH fiction? Woo-woo! Ever think there was homoerotic gazes happenin' between Mulder and Krycek? Well, some authors sure made the most of it!
There is much more to say about fan fiction, but it's better that you just go and see what I mean:
Unsorted assorted links:
Order of the Blessed Saint Scully the Enigmatic (OBSSE)