If you're just starting out and want to feel your way around, parallactic has a very nice informal guide to genfic here.

Godric's Hat Archive has a lot of very good stories. Check out their forums as well, for lots of fun discussions.

Potions and Snitches is an archive which focuses on Snape and Harry genfic.

Storytellers is a new multi-fandom genfic archive. Their HP section can be found here.

The Wizard's Playground is an archive specially meant to host stories appropriate for children aged 6-12, so it's conducive to genfic by its very nature. Check it out, and if you know any kids who like HP, then you know where to point them.

If you're on LiveJournal, there are several places you can go to get your gen fix. The HP genfic masterlist aims to catalogue good genfic through multiple recommendations. genfic_hogwarts, hp_shipless, hp_genrecs, and gen_fen (which is multifandom) are all communities for posting fics that aren't centered around relationships. omniocular is a new moderated community where good genfic writers can post their stories. It also issues challenges. hpgen100 is a community for gen drabbles. quibbler_report is a recsletter for HP gen and rarepairs. And hp_gen_ch holds a genfic challenge every month.

If you're interested in reading the results of genfic challenges, you can try Saeva's gen ficathon, which is old but good, the femgenficathon, which issues challenges every once in a while, and jennyo's Female Gen Ficathon, which is multi-fandom and includes several HP fics.