Adventure (esp. w/puzzle elements...Zelda, Metroid, Shadow of the Colossus), Arcadey Racing (Mario Kart, Burnout), Platforming (especially extremely difficult but precision-control 2D ones, such as the MegaMan Zero series or Super Mario Bros: Lost Levels).
I enjoy FPS and strategy games in limited numbers (genres are too oversaturated and so I only pick them up on occasion- FPS is more saturated, but strategy requires too much time to get skilled at, so I limit my purchases of each).
I have a special place in my hearts for good or creative boss fights. Hence why I love Shadow of the Colossus, the classic Sonic and Kirby games, fighting Sephiroth on Kingdom Hearts II over and over, etc.
I make occasional exceptions and generally enjoy hybrids. Kingdom Hearts was mix RPG/Adventure, Portal was mix Puzzle (Adventure?) and FPS, Smash Bros was mix Fighter and Platformer, Metroid Prime was mix Adventure and FPS...