I've marked anything with spoilers (which are actually a little bit important to one's first experience of this show, imho), but most of these aren't spoilery for much, and none of them for the series ending.
Just Sleep, and Sleep, by maestro1123
Evocative and very appropriately Sam, with the addition of perfect Gene and Annie voices. I'm a little startled that this didn't happen on the actual show, exactly like this. Warning for kind of intense themes.
I want to go home.
What's Expected, by alone_dreaming
This author is a rarity in any fandom, but particularly in one like LoM. She's perfectly capable of writing men who sound and act like men--and of writing someone as coarse and foul-mouthed as Gene Hunt the way the show does it. Also, she writes gen friendship! *fangirls*
This story is hard-core angst with an icing of h/c...typical fandom fare, but done the way the show would do it. I adore it. The first time he’s injured on the job (outside of the bruises when he conflicts with his DCI), Gene doesn’t sit with him like a great, big, weepy Nancy.
Immortality, by alone_dreaming
Drunk!Sam considers Gene, and Gene's resemblance to Dionysus. It's not actually crack, just a very realistic drunk pov, funny and touching by turns. Utterly gen. <3
Think Big Thoughts but Derive Small Pleasures, by lozenger8
This one *is* crack ("cracky buddy cop gen" she calls it). But the voices are so perfect that I don't care.
It was around three inches tall, with a rumpled suit, and a furious expression. Sam gaped, his mouth wide and his eyes fixed. “Gene?”
Just A Note..., by fern_tree and xiilnek
Fan fic meets fan art in this exchange of notes between Gene and Sam. Hilarious, complete with almost-NSFW doodles drawn by Gene to annoy Sam, and internet in-jokes on Sam's part that Gene doesn't get at all.