Only 2 Genres... brutal but lets see if I can narrow it down to only two...
First I would say 2D platformers is my favorite. Pretty much what grew up with and I still actively enjoy, Marios, Sonics, Metroids, Ninja Gaiden and newer titles are really good like The Messenger, Cyber Shadow and Spelunky. That is my bread and butter.
The Second Genre I would say would be Turned Based Strategy. Again I grew up playing Master of Monsters and Shining force into the early ours of the mornings with my friends when I was in middle school. Some of my favorite newer titles like Wastelands 2 and 3, The X-com games I love. Just finished Marvel Midnight Suns which was quiet excellent.