Let's brainstorm this!
ETA: My final lists, after the cuts.
Five of my favorite genfic stories about our stalwart Watcher.
theblackmare: The Bird Bone Flute (WIP)
How did Rupert Giles come to be the kind of man who could train Buffy Summers to be the greatest Slayer in history? Blackmare picks up with Giles unhappily working for the Council, having crushed the greater part of his spirit down to atone for his mistakes as Ripper. The Council sends him off to collect documents from an abbey that will soon be closed, and his journey begins.
headrush100: "Free Will"
Giles, dealing post-Chosen, by wandering from one Benedictine monastery to another in Europe.
madpoetess: "The Waking"
Rupert Giles and... a tree.
meegat: The Vulcan's Bane series
Someone has finished reassembling an artifact that was reputed to grant immortality to its possessor. The first thing the artifact does, however, is kill two people. Someone rather unpleasant who knows what it truly is is after it, however. Can Giles solve the puzzle first? This story has two sequels, exploring what happens after the most inventive setup in the first.
Vatwoman: The Watcher series, Giles/OFC, FRAO in part (unfinished)
Giles, in England through season 6, and two ghost stories. And a vampire story. And the new friend that was so statistically impossible for him to have made.
Five stories pairing Giles and Buffy.
A. Manley Haight, Autumnal Equinox, FRAO
Buffy is called to participate a rite of passage coinciding with the fall equinox. But her mother won't let her, and the drive is beginning to be too much for her to take. Includes one of the hottest phone sex sequences I have read.
gileswench, "A Mile in his Moccasins", FRAO
The inevitable bodyswitch story. Buffy, grumpy with Giles for having left her to go back to England, doesn't listen to his pleas for caution, and the weird demon nails them. Can they each resist the temptation to make the other over? Can Buffy figure out where the off switch is on Giles' man-part? Can Giles cope with a day on the job at the Doublemeat Palace? And then...
Kris Wahlberg, The Transformations Quartet, FRAO (unfinished)
One of the big Giles/Buffy epics. Picks up where season 3 ends, and goes in a direction very different from canon. This Giles has a very interesting backstory with an evil Council.
Reni: Baby Love
Giles has come back from England to beg Buffy to let him retire. Just as he arrives, the Legion of Dim strikes with a new experimental weapon, and turns the four Scoobies into toddlers. Oh dear. Bath time, diapers, and Slaying all make for chaos while Giles & Buffy try to figure out what happened and get it fixed.
uberaeryn: "Raining on Sunday", FRAO
Cognac. Chocolate. Savoring. Signals.
Five stories with Giles paired off.
TweedEmpress: Et in arcadia ego, Giles/Jenny, FRAO
Giles goes on a short holiday to Mexico City on the Day of the Dead, and is visited by Jenny. He at last has a chance to tie loose ends with her.
glossing: "Make Way for Librarians", Giles/Xander
Giles doesn't have a car now that Spike smashed up the Citroen. Xander does.
janedavit: Behind Closed Doors, Giles/Spike, FRAO, dom/sub
Spike finds an interesting way to keep Giles from committing suicide after Buffy's death. And incidentally keep himself occupied.
47_trek_47: Tarnished, Giles/Ethan, FRAO
Giles is in England and adrift after leaving Buffy in season 6. Ethan is out to disprove Giles' theory that they don't have a relationship.
ljs: Investigations and Acquisitions, Giles/Anya
From my favorite G/A author, a stylish "comedy of manners, romance, and domesticity, and of demons and spies". Inspired by spy novels and classic mysteries. Includes some crossover with Spooks/MI:5.
Edited as I build the lists. Note that I welcome you to construct your own lists if you disagree with my choices! Post 'em to the community! The more great Giles recs, the better!