I tried to organise this in some sort of coherent manner and link to the best places to find all the possible fic so you have to do the least amount of searching. I hope you find it easy to navigate and please let me know if I can improve it!
Disclaimer: this is by NO MEANS a comprehensive list. I've barely scratched the surface of all the good stuff you can find on LJ and Portkey. It is decidedly biased since I can only recommend what I've read or heard about. Use this as a jumping off point and keep searching and clicking links and feel free to add anything I've missed in comments.
Many (but not all) of my favourites are listed here.
[In making this, I looked at my favourites on Portkey and I cannot, in good conscience, recommend any of those to human beings. WHAT WAS MY TASTE IN 2005? Oh, middle school. I am shamefaced.]
Nicole's favourite is The Paradigm of Uncertainty by Lori Summers (madlori). More fic at the PoU Yahoo group if you have an account.
Authors (I included Portkey profiles if it seemed like there were more or different stories there)
amethyst_j (amethyst_j on portkey) (also contributes to fanfict00bs [link below])
annearchy (Anne U on portkey)
anythingbutgrey (more fic under her harry/hermione tag)
avonlea_dreamer (bingblot on portkey) (also contributes to fanfict00bs)
calmacil_20 and herminia (Herminia on portkey)
fated_addiction (and a stray story here) (Kaze on portkey)
goldy_dollar (Goldy on portkey) (also contributed to fanfict00bs)
greydawning (also contributes to fanfict00bs)
jacyevans (Jacy on portkey) (also contributes to fanfict00bs)
kyc639 (also contributes to fanfict00bs)
napalmnacey (also has great fanart here [most on page 6])
potterlet (Lissanne on portkey)
scribooty (also contributes to fanfict00bs)
Stories (from authors that only have a few H/Hr stories, don't have archives I could find, or were recced by FYHH followers)
All Our Firsts, NC-17 - NatiFcs28
Definitions of Romance, PG-13 - edenfalling
Four Points, PG - LittleCreek and Musca
Fragments, PG - Goldy and Demosthenes (individual archives listed above)
One Half of a Happy Ending, PG - drunkendreams
Regret is Too Strong a Word, G - noblealice
ritual at dusk, PG - noblealice
the fearful passage of their deathmarked love, PG-13 - likeserendipity
this veil across my heart, R - corleones
winter love - youlooksick
with no room for a pardon, PG-13 - aragons
harmonic_erotic (WARNING: contains exclusively R and NC-17 fics)
-They also have a wide collection of Draco/Ginny, Ron/Luna, and Lily/James fic, but Harry/Hermione is by far the most popular and numerous.
Pumpkin Pie Archive
-This is great for finding one-shots of various genres. Fics are located under Files. I think you have to have a Yahoo account to access it.
DISCLAIMER: I have not frequented either of these sites so I can't vouch for their quality.
Fiction Alley (Harry/Hermione)
Harry Potter Fanfiction
Browse FF.net at your own risk.
FYHH Fic Fest
Recommendations from the Fest
Masterlist of Fic Written
harryhermione - general community
harrylovesmione - general community
xharryhermione - general community
hhrforever - general community
hghp - general community
harmony_daily - daily picture community
hhrart - art and graphics community
hhr_fanmix - fanmix community
Other Rec Posts
HarryLovesHermione.com fanfiction recommendations
girlnamediandra's Fanfiction Recommendations
Other Ship Business
Harry/Hermione Ship Manifesto (introduction to the ship and fandom [NOTE: written before HBP was released])
Harmony Forever Forums
Harmony Podcast (you can also subscribe on iTunes)
anythingbutgrey's Non-Canon Comment Ficathon (includes many non-H/Hr ships) [archived at the hp non-canon delicious -- harry/hermione tag]
anythingbutgrey's The Very End: A Potter!Wars Comment Ficathon (includes many non-H/Hr ships and characters) [archived at the very end delicious -- harry/hermione tag]
anythingbutgrey's At the Close: A Harry Potter Wars Comment Ficathon (includes many non-H/Hr ships and characters) [archived at potter wars delicious -- harry/hermione tag (NOTE: also includes the fills from 'the very end')]
anythingbutgrey's Harry/Hermione Friending Meme
UPDATE!!!: Is this giant list overwhelming to you? Start HERE!