Either Survival Horror, Beat 'em Ups or Hack 'n' Slash.
I've loved Survival Horrors since I played games like Clock Tower and Eternal Darkness, but as soon as I first played Silent Hill I fell in love.
As for the slashers, I played Devil May Cry and haven't really stopped loving the freedom to pull off seriously awesome combos, it's the same reason I love Beat 'em Ups; I love picking a character that works for me, learning all their moves and combos and then kicking ass. I don't do it online very often though, it's so much more fun when the person is sitting right next to you and you can laugh in their face, it reminds me of the old days when me and my brother played Mortal Kombat together and he would ban me from using Scorpion.