1- Shredder iPhone Chess
2- Diamenty which is basically Bejeweled, my favorite online game EVER!
3- Sudoku, the world’s favorite logic based number placement puzzle.
4- Checkrz aka Checkers!
5- i-Tiles: a memory game
6- Reversi: an abstract strategy game
7- Collapsing Blocks: falling blocks puzzle game.
8- Video Poker
9- iMineSweeper: the classic Minesweeper game.
10- iPhone Sokoban: a puzzle game where you have to push the boxes onto the target squares.

All of these games are web based as Apple still doesn’t offer any downloadable games.