I've got a long answer to a short question.  My favorite is a light gun game called Time Crisis 3.  Really fun.  For old-school stuff I like Galaga a lot.  I've never seen one in person, but I'd love to play a bullet hell shmup like Ikaruga or DoDonPachi on a real arcade cabinet, or a 2D fighter like Guilty Gear or BlazBlue.

2D fighters and shmups are best played with a real arcade stick.