I was going to recommend Professor Layton (if you like puzzle games), but there's a story there.
Here's a list of the little-story/no-story games that I have (not sure if they're what you want though):
EBA/Ouendan series [music]- There's not really a main story, but each song has an insignificant small story that you don't have to care about
Jam With the Band (JP/Europe exclusive) [music] - Not really any story, unless you count tutorials
N+ [platformer] - Great game based on a flash game, but a little buggy
Picross or Picross 3D [puzzle] - Fun, unless you don't like thinking.
Call of Duty series [FPS] - You don't have to care about the story.
Contra 4 [side scrolling shooter] - Fun, but INSANELY HARD (even on easy difficulty)
Geometry Wars [Asteroids-style shmup] - Arcade games are fun.
Sonic the Hedgehog [sidescroller] - As much story as a Mario game
Advance Wars [strategy] - Not really any story, really.
Kirby [sidescroller] - Good game, but might be too easy
Peggle [puzzle] - Good only if you don't mind the squinty graphics.
Clubhouse Games [card/etc game collection] - Fun with friends. Kinda boring alone.
Trauma Center series [surgery simulator] - There's a lot of story, but you don't need to follow it. Surprisingly fun.