Star Wars: Original Trilogy
Largely original trilogy and The Force Awakens. Lots of Leia/Han, and I'm open to Poe/Rey/Finn.
By the Grace of Lady Vader and The Ascension of the Queen by Alderaan21, ami-padme, and FernWithy
Wow. Just... wow. There's a lot of "Amidala never died" AU fic out there, and some of it is even readable. But no one's ever taken it to this extent -- created a whole, detailed, unflinching alternate universe around what could have happened had Amidala survived. (The first story is "The Empire Strikes Back" rewritten for the AU, with parts of the movie brilliantly integrated, twisted, echoed and reflected in a million different ways). It's not pretty, or easy, and happy endings come with a price -- in fact, it's damned dark in places, and I guarantee you'll scream in horror and race for the second story the moment you finish the first. But the duology is beautifully written, completely logical, and utterly absorbing; these stories will stay with you for a long time after you finish. (Mainly Anakin/Amidala and Han/Leia; many other familiar faces appear (although not always in the ways you'd expect, and I'm going to hell for that understatement), along with a few well-executed OCs.)
Estimated Time of Departure by Yahtzee
"It was suicide... We just didn't die." A lot must have happened between the destruction of the first Death Star and the award ceremony; Yahtzee not only fills in the holes, she patches together some of the plot while she's at it. A very cool look at the early bonding of Han, Luke and Leia -- in particular, the Han POV is rock solid, and Leia is handled really well as she copes with the destruction of Alderaan. Plus, Chewie is hilarious.
A Father's Heart by FernWithy
There's a lot of backstory we never got on both Leia and Vader -- what happened in the years between Anakin's transformation and the attack on Leia's ship? What interactions did a Senator and the Emperor's right hand have? And how did a girl that young get to be a Senator anyway? This story cycle takes a swing at those questions and hits a home run. Leia's story rings absolutely true, and her take on Vader -- and what remains of Anakin Skywalker -- is gorgeously executed.
Swallows and Amazons by irnan
Indescribably cute; Luke babysits the Solo kids for a week on Yavin. There is camping and bonus!Mara. Part of a much longer series, but can stand alone. Seriously. SO cute!
Trying Again by LTLJ
Another of those awesome stories set between Star Wars and Empire--someone tries to kill Han and steals the Millennium Falcon; Han, Luke and Leia have to find out who did it and why. Really nice details add verisimilitude, and LTLJ captures Han and Leia in particular perfectly.
bury my heart underneath these trees by morganoconner
"Before Rey leaves to find Luke Skywalker, BB-8 has something to show her." Puts the pieces together very well, if heartbreakingly.
road trip playlist by magneticwave
"Rey is XO of a piece of junk, her captain is a foul-mouthed Wookiee who doesn't respect people who respect authority, and there are pictures of naked people glued to the ceiling of the Falcon. She honestly couldn't be more thrilled." Heavy PG-13 because Chewie's every other word starts with F, but hilarious and a little serious underneath.
The Story of Finn by LullabyKnell
"The only thing Stormtroopers own are stories." Variation on a theme: Stormtroopers inspired by the "traitor". Strong OCs, particularly the narrator.
Tomorrow (there'll be more of us) by dimircharmer
"The resistance is starting to get stormtrooper defectors. Finn helps them out." Astounding adorable and every-so-slightly heartbreaking. Bonus!Leia.