iPhone and iPad apps tagged "two-player game."
Wild West Checkers - Same Game, Different Theme
Wild West Checkers is a slingshot-style checkers game where players attempt to shoot their opponents checkers off the board without losing any of their own. The second such iPhone app I’ve come across with the same principle, and coincidentally the same seller, Wild West Checkers is similar to iChapaev, but sports a wild west cowboy and Indian theme and a price tag of 2 dollars higher.
Knots: Tie Yourself Up with Free iPhone Game
Knots is like Twister for your fingers. Colored dots pop up on the screen and you hold a finger until told to release and stop on another dot. And, just like the original Twister, the longer knots goes on the more twisted you become and the more fun you have.