1. RPGs.
2. Strategy games.
I vastly prefer turn based strategy. Jagged Alliance 2, the Advance Wars series, Blackguards, XCOM: EW - I love games like that. I played a ton of RTS games too in my time, but playing SC2 Legacy of the Void and Grey Goo in the last 8 weeks made me wonder if I ever truly loved the genre. Or maybe those games were just meh. At least when it comes to the singleplayer experience, nothing will ever take away my 500 hours of loving the Dawn of War series online. But in SP, no matter how inventive the level design, at the end of the day it boils down to raising a critical mass of units and then sending the wave of death over the enemy base. I don't enjoy that as much as I once did back in the SC1 and C&C days anymore.
3. Adventures.
Just recently beat Life is Strange, it was fantastic. Day of the Tentacle. Classic Sam & Max (fuck Sucktale). Phoenix Wright.
But I can appreciate games from most genres. Several FPS games are among my all time favourites (System Shock 2, Half-Life), as well as Action Adventures (Tomb Raider, some Zeldas, MGS [not gonna consider stealth its own genre for this discussion, okay?], Resident Evil both classic and up to 5).
Some genres that just aren't for me are:
Platformers - there are exceptions like Mario 64 or Spyro the Dragon back in the PSX times, but especially these days, I can't get into them. I have like 50 unplayed indie platformers from various game bundles in my Steam library and finally decided to remove most of them from the list since I won't play them anyway.
Survival/Crafting Sandbox - Nope, I don't have any childhood traumas that I need to compensate for with virtual legos
Racing - I liked Burnout 3 and Dirt 2, but that's about it
Fighting - Don't enjoy playing against strangers online, boring as singleplayer experiences. Sure when a buddy is visiting it's fun to have a few rounds of some old NeoGeo game in MAME, but we usually have our fill after 30 minutes or an hour tops. Wouldn't buy SF5 for full price or anything like that.
Sports - See fighting.
Puzzle - I like Portal 2 as much as the next guy, but it's rare a puzzle game interests me enough to entice a purchase.
Shooters / Spectacle Fighters - Not my thing. Button mashy stuff is instant no-go.