1. (Japanese) RPG - Phantasy Star changed how I looked at games. If we can get detailed, grandiose RPGs with expansive settings and visionary storylines are my absolute favorite. But the genre is so deep and has so many different varieties of style... I can get games heavy on storytelling, I can get lighthearted anime romps, I can get games with heavily abstract gameplay systems, I can get biting dungeon crawls, I can get games with an emphasis on tactics and puzzle solving, sometimes all in the same game.
2. 2D Action/Platformer - I've always found level design to be a vital component of games, and these genres absolutely nail them.
3. STG - It's a favorite from when I was a kid, pick-up-and-play gameplay combined with heavy challenge and beautiful/memorable settings (in the best ones).
Fighting, puzzle (moreso the Sokoban-inspired titles than the Tetris/falling block titles), uncategorizable-genre games, marble-rolling games, are all up there too.