Epic-alert, but Separation Anxiety is one of the best Gilmore Girls fics ever written. Set in the summer following the fourth season, Lula Bo deals with the aftermath of that season finale with more care, insight and compassion than the show did. The language is beautiful, the characterization remarkable, and Luke and Lorelai's relationship is handled carefully, painfully, and ultimately perfectly. Everything I wanted to happen, happens as it should. Words cannot express the perfection of this fic (or how much the sequel, Everything Old Is New Again, rocks).
The Luke/Lorelai Ficathon
I love shaye for putting this ficathon together, as there can never be too much good L/L fic in the world. I particularly recommend the excellent offerings of thestickywicket, shaye, voleuse, jade okelani, mandysbitch and nestra (not necessarily in that order), but there's very little up there that's not good.
I love macha's take on Luke and Lorelai; it's often better than the show's, really. She specializes in post-eps like The Last Crazy Thing, which is painful in all the ways it needed to be, but the ending gives you something to hope for, back when there didn't seem to be anything. Also read Breakfast at Luke's, A Craving for Apples and basically everything else on the entire archive.
As hard as it is to find well-written Luke/Lorelai fic, it's even harder to find that fic written from Luke's POV. Kieyra manages both in Take Whatever You Can Get. Her Luke is wonderful, a gorgeous interpretation of what we've seen on the show, and his long relationship with Lorelai is laid out in train-of-thought flashbacks that ring absolutely true. The entire story was based in canon at the time, and works beautifully if you're a Java Junkie, or even just a fan.
A Concern for Dark Corners
In Megan's Something More, Lorelai makes one little phone call home from Europe, and everything changes. An excellent depiction of a Luke/Lorelai relationship -- long enough to work them through all the problems and pitfalls of friends becoming lovers, short enough to keep you involved until the very end. Megan has an ear for dialogue that doesn't quit, and her characterizations never falter; Fall is dead-on true to character for both Luke and Lorelai -- it could have happened this way, and wouldn't it have been neat if it had? Also try Washington for a great Rory and Paris fic, then start browsing your way through the many fandoms Megan plays in.
Of Trees, Diner Men, and Breaking is another take on the original Luke/Lorelai breakup, angsty AU and proud of it. Depressingly true to everyone concerned.
Pretty in the Morning centers around Rory and Jess and a bed -- but the fun is how Luke and Lorelai cope. It's a short, sweet fic about the pitfalls of parenting.
Nowhere to Hide is a Standard "Lorelai gets a clue" plot, but written well, with dialogue that could be straight from the show, and a strong Dean/Rory/Jess subplot. When It Gets Down to It is also a solid L/L story.
In The Morning After the Night Before, she writes Luke and Lorelai finally getting a clue backwards, which somehow just makes it all cooler. Dead-on dialogue, the best Luke characterization I've ever seen, and a ton of happiness for those Luke-Lorelai shippers who spent years beating their heads against a table.
Crash Like Thunder by Keren Ziv
A wedding and a child (order optional). A brilliant Lorelai POV on another way things could have gone following her estrangement from Rory. A slow and bittersweet view of Lorelai's marriage to Luke and her relationship with her mother and daughter, every word chosen perfectly.
Like a Second Chance by Nestra
Short, insightful, gorgeous Luke/Lorelai fic. The dialogue feels just like the show, but without that nasty aftertaste.
The Presence of Absence by Holy Lulalicious
"'I love you,' she says simply. She doesn't know if it'll matter, doubts that it will fix anything, but she's learned tonight that she can have the strength she's always thought she had if she's willing to be weak for just a moment." Very good, if quite angsty, L/L.
A Study of Motherhood in Black and Gray by aj
Emily looks for ice cream and thinks about the things her daughter knows how to do. A deeply insightful Emily fic, slow and rich.
It's Right There is one of the longest Luke/Lorelai fixes I've run into, and up there with the best. CoffeeDrinker takes her time, lovingly building the relationship from the point when Lorelai finally takes off the stupid blinders! Great characterization, appropriate levels of sweetness and worry -- guaranteed to leave you all WAFFy and happy. And, god help us, there's a sequel.
Stew Pid at Fanfiction.net
Season 3 as I have it isn't actually a season 3, since most of it takes place during the summer, but Stew Pid put together a series of 15 'episodes' picking up after the Gilmore Girls season 2 finale, and they are good. The dialogue is perfect, the voices coming through clearly enough to make up for the script format, and the issues are addressed with the show's trademark mix of drama and humor -- you could film this and have a pretty good season going. Way not for the anti-Jess crowd if you're still intent on hating the kid; anyone else who enjoys Gilmore Girls should get a kick out of it.