Trace. Even saying it kicks off the soundtrack in my head. One of the first games I downloaded for my daughter to play, Trace allows children to problemsolve while playing, as they work to get a little red stick man on a journey to the sun. Each "world" (volcano, flame, water, space, etc.) initiates a different background setting, with its own theme tunes and challenges.
Your job is to trace a path with your finger around a landscape with various moving obstacles. Each screen gets harder, but small achievements along the way make it very satisfying. You can erase errant lines, hop over gaps and try as many times as it takes to achieve success. This is one game we come back to time and again.
You'll like it because: As fun for adults as for children.
Too bad: The soundtrack will stay in your head long after the game is shut down.
iPhone Apps users gave it 4/5 stars