Outside of FPS, then, a "short" list of single player games I've thoroughly enjoyed:
RTS: Homeworld 1 (remastered version will be out soon), starcraft 1 and 2
Turn Based: X-com: Enemy Unknown (Or the original, UFO Defense if you're feeling hardcore), Civilization (any of the numbered series + Alpha Centauri)
RPG: Star wars: Knights of the Old Republic, Neverwinter Nights 1, 2, Wizardry 8, South Paark: Stick of Truth, Bard's Tale, Cthulu Saves the world, Planescape: Torment
Point & Click adventure: +1 on Grim Fandango, The Longest Journey, Monkey Island 1, 2, 3, Deponia Series, Gone Home (technically first person)
Puzzle platformer: Braid, Fez, Limbo, Trine (1&2), Gunpoint
Platformer: Psychonauts, Rayman Legends or Origins, Spelunky, Guacamelee, Super Meat Boy, La-Mulana
Puzzle: World of Goo, crayon physics deluxe
3rd person Action/RPG: Dark Souls 1, 2, Deus Ex: Human revolution (or the original!), Mass Effect
Isometric Action RPG:, Bastion, Torchlight, Path of Exile (technically an MMO, but easily played single player)
Survival Horror: Amnesia: The Dark descent....I love horror games. IMHO this is the best horror game ever made. No other horror game has come close to scaring me as much (except the original alone in the dark, but I was 13 at the time and it hasn't held up well over the years). Most of the other decent ones rely on jump scares. This is the only game I've ever needed scotch to finish.
Oh, and I'm assuming you've already played portal 1 & 2. If not, start there.
Cheers!