A bit about my preferences, though, just so you know what sort of recs I'll be putting up here.
1. There are a ton of potential pairings in the Potterverse, mostly due to the large number of characters in the books. And I'm open to most ships, with a few exceptions, but here's a list of ships that I get genuinely excited about:
Snape/Hermione -- my favorite by far
Neville/Ginny -- especially since OotP came out
Draco/Ginny -- only as a secondary pairing
Ron/Draco -- my second favorite
Ron/Harry -- the quality of these stories is often impressive
Harry/Draco -- this one snuck up on me out of nowhere
The only pairings I absolutely won't touch with a ten-foot pole are incest and Snape slash. Incest, well, for obvious reasons, and Snape slash... I simply see Snape as a heterosexual fellow and am not able to suspend my disbelief long enough to read otherwise.
2. Oh, my, the Mary Sues we often encounter in this fandom. I mean, they're pretty bad in other ones, but in the Potterverse, when we can give ourselves magical superpowers in addition to our bubbly personalities and beautiful hair, we've got a veritable infestation. Having said this, though, it's mostly confined to the fanfiction.net and Fiction Alley sites.
3. I'm pretty bad about not liking the classics in this fandom -- I'm not a big fan of Pawn to Queen, Cassie Clare's Draco Trilogy, or Underwater Light. Sorry. Although having said that, I am fairly fond of a couple of the classic slash fics out there. One in particular that I would wallpaper my living room with if I didn't think it would result in institutionalization.
4. Lots of WIPs in the Potterverse, which stinks, but what can you do? It just means that there are a handful of excellent stories out there that I'm following, but haven't been finished yet. I'll let you know when they're done, though ::g::
Enough babble -- go, read!
Hayseed