Well, I came to the Writing thread late, so I'll poke my head in here late too <g>.
I read fanfic for everything. If the show/movie/etc interests me and I have some remote idea who the characters are, assuming the fanfic is well-written I'll probably give it a shot. I've read fanfic for shows I've never seen <g>. I'm sure most of the references go right over my head, but if it's well written I generally enjoy it (although a well-versed fan might enjoy it more).
Usually I'm drawn to these fandoms because I've fallen in love with the show/movie/etc. I can't not read about them. Some character or concept or relationship just fascinates me. If I feel like I know the source material well enough I might try to write my own, but for shows where I haven't seen all the episodes I'm generally content just to read.
And on occasion I'll follow a good writer from fandom to fandom if I particularly like his/her work, even if I'm not at all familiar with the new fandom. Years ago I followed a FoLC writer into Star Trek TNG and became a fan of that too <g>.
Anyway, most commonly I read L&C, but I read Star Wars, Gargoyles, and Beauty and the Beast (the TV show) fairly often. Star Wars has a lot of fanfic but the average quality is relatively low. Gargoyles has relatively little fanfic and the average quality is still relatively low; there are a few amazing authors there, but you have to sort through a lot of dross to find them. Beauty and the Beast has a lot of fanfic, but because the fandom predates the Internet a large portion of it is only available in printzines. And very few fandoms have central archives the way that we do (and none of those I've come across have GEs!), so it's harder to find fanfic there than it is in FoLCdom.
In the past I've dabbled in Star Trek TNG, X-Files, Smallville, the Matrix... I'm sure there must be some I'm forgetting.