I'll put this under a cut so people who haven't read the books yet but want to won't get spoiled. This is going to be a pretty big list, by the way, so settle in:
Something Special (Beautiful) by youcantseeus--It was pretty much spelled out in the books that some victors get pimped out by the Capitol. In this fic, Peeta is the one getting pimped out. He meets up with Finnick Odair, and the two share some home truths. Recced because: It's incredibly well-written and believable why Peeta's getting prostituted instead of Katniss. The dialogue and the world-building are perfect. Not exactly a fluffy fic.
Smoke Rising by AngelProjekt--How do two incredibly-damaged people like Peeta and Katniss manage to form a relationship after everything? This is a Peeta POV on how it happened. Recced because: It avoids the Nice Guy (tm) Peeta trope I've found is all too common in the fandom. He's damaged and bitter, but, at the same time, he manages to find hope. His feelings for Katniss are complex, but he's neither a martyr to her nor superior.
Battle Scars by LadyOfSpring--Effie and Haymitch survive, as they always have. Recced because: The author made Effie/Haymitch work. She made it work! And without sacrificing anyone's character. You know that means the relationship isn't fluffy or even approaching healthy. There's much sarcasm and drinking. But it works, and that's the marvel of this fic.
There's Another River on the Other Side by Mithrigil--Katniss dies instead of Rue, and Peeta dies without Katniss. Rue and Thresh win the Games--and inherit the Capitol's ire. Rue becomes the Mockingjay. Recced because: It's a great look at what might have been, and it's told so beautifully and so believably. There are appearances by Haymitch and a few other familiar faces as well. This one gave me chills. Rue's pov is so powerful in this author's hands.
Wisely, I Say, I Am a Bachelor by Mithrigil--A character study of Cinna, and of Finnick through him. Sexual violence, so be warned. Recced because: It's a great study of Cinna and Finnick. Cinna/Finnick is a popular, and totally understandable, pairing. This fic gets behind both their eyes and into what makes them tick, and why Cinna rebelled. Portia gets some great scenes, too.
Out of the Night: An Interview with a Mockingjay by athousandwinds--This one's a bit lighter. A reporter finally gets Katniss, after the war, to agree to an interview. Recced because: It's not that what Katniss has to say is funny, but I love the look at post-war media in Panem. There are some really great digs at the media in general, and a great study of Katniss as she might be years down the road.
To the Victor, the Spoil by Annakovsky--Katniss wins her Games, but alone; she reflexively kills Peeta when he pulls out his knife at the end. The Mockingjay dies in the egg, and Katniss is forced into the mold of a Victor. Her body is sold to the wealthy, and her soul is broken by having to mentor doomed children. Recced because: It's pretty pitch-black, but believable. It actually contains Haymitch/Katniss, which is a pairing I find squicky as hell. It works because the author also finds it squicky as hell, but in context? It's her only resort as her life spirals downward. It's almost entirely told from Haymitch's pov, with guest appearances by Cinna and Finnick.
Foxglove by Annwyd--Twelve-year-old Cinna makes an unexpected connection with a contestant in the Hunger Games, and it sets his life on the path that will lead to his actions in the books. Recced because: It totally makes sense, the way this happens. His native compassion, at a tender age before the Capitol can take it from him, comes up against the horror of the Games and the callousness of the Capitol citizens, and he becomes something better as a result. Also features Finnick Odair.
Happy reading!