I'd say shmups is a good way to increase dodging skills, precise motion, and the ability to look to the whole screen. Pretty useful in a lot of action games.
Besides, Unison improved my memorisation skills. I was pretty good at memorizing sequences of buttons, but several minutes of DUAL stick motions to memorize is more challenging.
As others have already said the truest answer to this question is Counter-Strike. I always try to play for a half hour before i start playing another FPS like Battlefield or Shattered Horizon. It's so easy to just destroy players in those games after warming up with CS.