Not sure I really have a specific genre, but I do enjoy some types a bit more than others. I guess if I had to list any favorites, this is what it might look like:
Legend of Zelda
Okami
NieR
Fallout
Halo
Red Dead Redemption
GTA
Saintts Row
Super Smash Bros.
Sonic
Mario
Donkey Kong
Metroid
Metal Gear Solid
Any of Suda51's games
So I guess there's a lot of adventure games, RPGs, or sandbox games, mixed in with platformers and FPSs, and one stealth game as well as one fighter. Of course I've played a lot more than just these, though, and a game isn't necessarily defined by its genre. You even have some that mix a bit, my favorite being RPG elements put in, well, pretty much every game ever. 
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About suffering they were never wrong,
The Old Masters: how well they understood
Its human position; how it takes place
While someone else is eating or opening a window or
just walking dully along...