Harry/Ginny and Ron/Hermione tend to rule my recs, but I also love long epics that trend much more to the gen side.
After the End by Arabella and Zsenya
One of the definitive Harry Potter fics. Established, fleshed-out recurring and original characters trying to deal with normal life after fighting to save the world. [When you're done, try Hermione, Queen of Witches, the first four books rewritten from Hermione's point of view.]
Harry Potter and the Curse of Durand by Nomad
"When Harry returns to Hogwarts for his sixth year, he finds the entire school under an ancient and deadly dangerous enchantment." Great plotty, gen fic from the always awesome Nomad.
Harry Potter and the Silent Siege by swishandflick
Intricately plotted (occasionally too much so) sixth-year fic, epic-length and well executed. The completed sequel, Veil of Memories, is possibly even better.
The Shadows of Silence by Myth & Legend
Well-plotted, well-written, neatly plotted sixth-year story from Harry's POV, spinning off threads for a sequel. Harry's relationships with his friends and family are nicely drawn (particularly his growing friendship with Ginny), and all of the characters ring true.
rabbit and ~v~Jinx~v~
Slytherin Study Group is one of those fics you probably don't want to read in public, unless you enjoy experiencing the same humiliation that's gifted to the fourth-year Slytherins (and, eventually, their erstwhile enemies). A truly classic Marauder-era series of silly fics, with everyone involved so plausibly and hilariously portrayed, it's impossible not to see it happening. Including the sheep. Especially the sheep. (If you want some present-era snickers, try Knowledge Is It's Own Reward.)
Balance by rabbit
And once you've read Slytherin Study Group, you'll get a few of the references in this truly outstanding fic -- rabbit is my new HP hero/ine. The students must rally to help the teachers after an attack leaves the school in a rather strange -- and scary -- situation. Harry and Draco are forced to work together with some of the best characterization I've ever seen for either, and the visitors to Hogwarts will leave you stunned and cheering. Intricately plotted, breath-holding suspenseful, richly atmospheric, and detailed down to the last torch, toad and broomstick. Absolutely wonderful and one of my favorite HP stories ever, and complete! New Link
Naked Quidditch Match by Anya McLerie
A game of magical Truth or Dare gets out of control, and everything else gets out of control from there. A brilliant parody told almost entirely in 'Mmail' messages between all parties concerned (and a few that get dragged in purely for the hell of it), written with great affection for the universe by a mind determinedly dwelling in the gutter, and eager to take you down, too.
Registration by Sam Vimes
When they get roped into waiting to register James' unborn son for Hogwarts, Sirius and Remus have a long day's wait, and a small dilemma -- nobody's picked a name yet. Featuring several parents, one Weasley, some cinnamon buns, a very long line and quite a few giggles.
Harry Potter and the Battle of Wills by Jocelyn (and Mum)
One of my all-time favorite sixth year AUs. There is, perhaps, a bit too much crying, but otherwise, it's well-plotted, the characterization is good (Snape in particular) and the feel of the world is right. The pacing gets a little weird at the end, but the finale is well worth it. Largely gen; canon ships only in passing.
LavenderBrown @ Fanfiction.net
The Book of Morgan Le Fey is Ron's POV; as he falls more in love with Hermione, he must first win the girl, then figure out how to do things from there -- without flunking classes, getting killed by Death Eaters or Dementors, or going completely mental in the process. Very well done epic and there's an equally strong sequel.
Melindaleo @ Fanfiction.net
The Seventh Horcrux is an excellent novel, and a satisfying end to the Harry Potter series (far more so than DH for me). (Melindaleo makes one character choice that is highly debateable, but quite justifiable IMO, particularly within the bounds of this particular story.)
The Sugar Quill
My Harry Potter fanfic site back in the day. Ron/Hermione and Harry/Ginny rule the day. Some Remus/Sirius slash, but very few other ships. There is also some incredible fanart (particularly Tealin and A.L. Sauveterre).
Aquae Sulis by Honeychurch and Lallybroch
Ron/Hermione-centric story with an adventure plot; sweet, but not schmoopy.Harry Potter and the Fifth Year from Hell by Angua
An abandoned fifth-year WIP, but well worth reading.Points of No Return by Night Zephyr
Ron POV fifth-year epic: he's developed a new power, but with it comes a responsiblity that could get him and his friends killed, when his new-found skills come between Voldemort and his prey. And then there's the thing with Hermione....A Simple Request by Violet Azure
A simple, lovely visit inside Remus' head in the days before he was reunited with Harry, when he still believed his best friend had betrayed everyone he ever loved.
Fiction Alley.org
A mountain of Harry Potter fandom, sorted into four houses of fanfic and one of fanart. Extremely heavy on the slash and UCs (Harry/Hermione, Harry/Draco, Hermione/Snape and Remus/Sirius are popular) for those of you into it; if that's not your thing, keep looking anyway -- gen treasures for both present-era and Marauder-era abound.
Broken Fate by Qui_Xux
From a future where everything went terrible wrong, four desperate children travel back in time to stop Voldemort's ultimate victory. Some of the parentage is predictible, some will keep you guessing, and the final epic hangs together surprisingly well; pacing goes by the wayside a time or two, but gets back on track.Harry Potter and the Labyrinth of the Mind by Sandy Phoenix
Sixth-year fic, niftily plotted and strong on emotion, without going as far over the edge as OotP did. The OC gets too Mary Suish for my taste, but serves her purpose; the plot is tight and moves quickly, with strong action scenes and no punches pulled. Mild Ron/Hermione.Prongs Rides Again by BrieflyDel
One Halloween night, James and Lily Potter were murdered.... or were they? 13 years later, a stag finds his way to Hogwarts, and the world as everyone knows it changes. A lovely, almost poetic story of James' return.The Speculum Curse by Hyphen
Slytherins cast a personality-altering curse on Seeker James Potter the night before a major Quidditch match, and the other three Marauders are determined to free him from the effects -- no matter what it takes. Obviously, Wacky Hijinks Ensue.
PhoenixSong.net
The most reliable Harry/Ginny fix on the web, among other fics. Lots of fluff to be waded through, but several very solid stories as well, and a few absolute gems.
Bludged by Shay Caron
A little bit of Harry/Ginny, featuring an excellent Quidditch match, unrealized feelings, and a really nasty Bludger attack. Fluffy as hell.The Great Towel Trick by Allie Kiwi
Fluff, fluff, fluff, but very funny fluff.Heal the Pain by aibhinn
One of the more original takes I've seen om After the War; Harry joins the Department of Mysteries, and he and Ginny struggle to cope with their losses. YMMV: There are some gratuitous plot elements that could have been dispensed with (Ginny Sue makes an initial appearance), the angst levels run insanely high, and the title is appalling, but overall, it's an involving romance with enough well-written action to keep it moving, and some really unique looks at the wizarding world outside of Hogwarts.
The Hidden Tower
Showcasing the work of writers Casca and Emmyjean (plus a few guest writers). The page layout isn't great, but the fic is largely solid.
The Beginning of the End by Casca
"Spans the course of Harry's seventh and final year at Hogwarts, detailing Harry's struggle with the path that has been chosen for him and the roles his friends play to aid him in the ultimate defeat of Lord Voldemort."Crossroads by Emmyjean
"In her seventh and final year at Hogwarts, Lily Evans finds herself facing a tragedy that leaves her life in pieces. In her struggle to find her way in a suddenly unfamiliar world, she finds strength she never knew existed -- both within herself and in a boy she'd always thought she'd known." Very believeable Lily/James relationship. Also try her Iris for a solid, if heartbreaking, Remus fic.Seeking Ginny by Casca
AU after OotP, but Casca rewrote this story to include the Ginny who was revealed in the last three books. A strong exploration of the Wizarding world outside of Hogwarts, with well-done original characters, and complex relationships. H/G from an adult Ginny point of view; she really has to work for it.
A.J. Hall
Kiki made me read this. Lust Over Pendle is Draco/Neville slash, but don't be fooled, because that's not what the story's about (it's also not about Harry Potter). It's about love and friendship and adventure. It's about what, exactly, a recently reformed supervillain does with no income and a bloody big ancestral manor to upkeep. It's about kidnapping, mental disturbance, Dudley Dursley's girlfriend, house-elves, cave crawling, the downsides of being the Loveliest Witch in Britain, daring rescues, percentages off the top, and what beer to order in an English pub. It's about some of the most hilarious narration to be found in modern literature, it's about the size of a novel, and it's about the funniest thing I've read in quite some time. A.J. has quite the gift for making unlikeable characters likeable without taking them out of character (annoyingly for me, s/he also does it in reverse upon occasion), so give it a try. Trust me. (Then, give everything else A.J. has ever written a try, including the HP/Vorkosigan crossovers.)
Marina Frants
I'm mostly into Marina for her fabulous Harry Potter fic, particularly Harry Potter and the Polka Dot Plague, a wonderfully well-plotted and characterized fic starring Harry and Snape; you won't see most of the twists coming, but you'll enjoy every moment spent both in Harry's head and in Snape's. Worthy of J.K. Rowling at her best. She also writes Buffy, Highlander and a few others.
sunshyndaisies' Harry Potter Fan Fiction
Knight of the Death Eaters and the sequels star Ron as a top Auror fighting the evil that is still haunting the wizarding community. Solid writing, and the second generation of Weasleys and Potters are well-drawn without taking over the story.
Aftermath by Shezzly
Fluff and makes no pretense of being anything else, but threaded through the sweet Harry/Ginny romance is a pretty solid take on the repercussions of the end of the war with Voldemort, life after school, and of falling in love with the only daughter of the family you're currently living with.
Backward With Purpose by Deadwoodpecker
A "time travel to fix the pyrrhic victory" story. Highly angsty in many spots (I debated for a really long time whether to rec it), but it's reasonably well done. Canon ships, very heavy H/G.
Beyond What Came Before by Shezzly
Seventh-year Ron is dead on target -- clueless and such a guy, but sweet and willing to figure it all out -- and there's also a solid Hermione and a quite good Draco. The plot is perhaps a little thin, but considering it's so not the point, it's pretty good.
Bury the Hatchet by Silver Phoenix
Seven years ago, three students defeated Voldemort. Now, Hermione Granger is a professor at Hogwarts and trying to forget that final battle -- until a threat to Dumbledore brings a familiar face blasting back into her life. Good future R/H fic; nicely plotted, and the original characters are a treat.
Death Before Dishonor by Robin
Fifth-year fic, beginning in the summer and told largely from the points of view of the adults, as Remus and Sirius scramble to protect the children, rescue Snape, fight Voldemort, and raise as much havoc as wizardly possible at their alma mater.
Fellytones and Fuzzy Slippers by The Treacle Tart
"What will a wizard do for love? Apparently humiliate himself - daily. Harry, Ginny, Ron and Hermione alone in the country. Who thought this was a good idea?" Not the best writing ever, but funny, with many sharp and hilarious comments on men, women and idocy in all its manifestations.
Find Strength In What Remains Behind by Lanna Michaels (lannamichaels)
"Dear Mr. Potter, we are pleased to inform you that you have been accepted at the Merlin Memorial Academy For Magical And Muggle Squibs." Spare and absorbing AU.
Ginny's Gift by Ashwinder
An unexpected birthday present from Ginny to Harry sets in motion a chain of events that changes everything. Solid seventh-year au; the sequel, The Long Road Home is also good.
Harry Potter and the Bookwyrm by Jelsemium
A short second-year fic with guest appearance by Sirius and, of course, the Bookwyrm.
Harry Potter and the Song of Night by QuizzicalSphinx
A tangled, twisted and downright intriguing sixth-year novella. Crackling dialogue and characterization, very clever narration.
A Harry Situation by Jelsemium
Excellent dialogue and well-handled UCs in a summer-before-fifth year fic. The last several chapters are a bit tacked on, but fun.
The Home Series by Mosylu
A sweet, but never sappy, series of Harry/Ginny post-Hogwarts fics (link goes to the first story, written long before DH). Desk Duty is hilarious: when beseiged by a toadlike High Inquisitor, a librarian's got to do what a librarian's got to do.
Innocence Lost and Found by Iniga
An unusual summer-before-fifth-year novel, centering on Remus, Sirius and Harry. As Harry's situation with the Dursleys deteriorates, Sirius is caught between proving his innocence and helping his godson -- three guesses to how he chooses. There are two well-done sequels, one fo them Percy-centric..
Just a Random Tuesday by Twisted Biscuit
Minerva McGonagall survives another very long day under Umbridge's reign. Dead-on McGonagall voice and Hogwarts insanity (including lots of minor characters who rarely get such a good treatment); you'll feel total sympathy for her even as you're cackling gleefully at the chaos.
Kiss the Girl by Fleur
Could not be fluffier if you beat it with a fluffy stick. Everyone at Hogwarts is tired of watching Ron and Hermione dance around each other, so they band together to get the pair to do something about it already! Ginny and Harry are predictable, the other fifth-year boys are amusing, Fred and George are a little terrifying, and even the professors get dragged in, but things don't become truly surreal until Draco joins the act. And he's got at least 209 really good reasons to help....
A Library with a View by The Treacle Tart
"Ron sits in a hospital bed and thinks about life after war."
Midnight by the Weasley Watch by excessivelyperky
The great thing about having the same taste as a writer you respect is being able to pillage her rec list; Nomad led me to this story about Ron Weasley, Severus Snape, and chess. I didn't think a story consisting of an endless number of chess games would make fascinating reading, but excessivelyperky has an excellent touch for writing Ron (which I'm a total sucker for), and creates a sympathetic, yet still completely in-character Snape (which isn't so much my thing, but which I respect). Two lovely original characters and a bit of suspense round out a remarkably strong story. Give it a shot.
Promises Unbroken by Robin
Strong AU that takes off from one little point -- Sirius was the Secret Keeper. A completely different universe, wih adult Potters and entirely different challenges for their son. Updated to reflect some continuity from HBP.
Sugar Quill Maneuvers by Alchemine
A short encounter between two characters you wouldn't think of, and the fear even teachers feel. Marauder-era.
Summer Holidays by Penknife
Hermione, after the war.
Thirst by victoria p.
An interesting look inside Snape's head, and through his eyes at the Terrible Trio -- one member in particular.
Untitled by ink-splotch
"What if, when Petunia Dursley found a little boy on her front doorstep, she took him in?" As much meta as fic, but an excellent au character study
The World As We Knew It by Lady Alinor
Harry is transported to an alternate universe, where a first-year Ginny was sentanced to Azkaban. Obviously dark fic in places, but also nicely well-executed, and a good, long read. Harry/Ginny.