Platformer - Super Mario 64 (one of the best games of all time imo)
Puzzle - Portal
RPG - Dragon Age: Origins
Action - Uncharted 3: Drake's Deception
Fighting - Super Smash Bros. Melee (don't like the genre much, but I had some good times playing this with my friends back in the day)
MMO - RuneScape
FPS - BioShock Infinite
Rhythm - Kingdom Hearts: Melody of Memory
Adventure - Gone Home
Racing - Jak X: Combat Racing (not a huge fan of racing games, either, but at least Jak X has some great character-driven storytelling)
Sports - Backyard Sports: Baseball 2007 (literally the only sports game I have ever owned)
Mobile - Nier Reincarnation (only just started, but it's already the most impressive game I've played on mobile, by far)
Survival Horror - The Last of Us: Left Behind
4X - Ugh. Sid Meier's Alpha Centauri, by virtue of it being the only 4X game I've ever played. But I could not possibly hate the genre more.
Tactical/Strategy - Star Wars: Galactic Battlegrounds
Sandbox - Elite Dangerous
Visual Novel - Analogue: A Hate Story
Stealth - Sly Cooper: Thieves in Time