Title says it all. If this is a repeat topic then feel free to redirect / combine / delete.
For me it's a tough choice between fighting games, platformers, and action/adventure games, but ultimately I have to go with platformers. Games where you control running and jumping cartoon characters are about as video-gamey as you can get. Mario, Sonic, Mega Man, Donkey Kong, Rayman, Ratchet, Jak, Sly, Meat Boy, you name it. I love me some platformers.