The other genres I play in order of most played.

RPG
I love them. Alone or with friends, doesn't matter much, it's my favorite type of games.
Favorites: Final Fantasy Tactics, Suikoden 2, Final Fantasy 5, Final Fantasy 6, Ragnarok Online, Final Fantasy 4, Chrono Trigger.

Fighting/Beat 'em Up
I only play these with friends but it's so much fun.
Favorites: Soul Calibur 2, Super Smash Brothers Melee, Tekken Tag Tournament.

Strategy
From time to time I'm addicted to one.
Favorites: Seven Kingdoms 2, Age of Empires 2, Metal Knights.

I also play some other games like the Mario and Zelda games.