Since the iPhone is such a casual-friendly device, it's the perfect candidate for the sorts of games that might usually be found on the pages of a newspaper. Word searches, crosswords, Sudoku and the like.
With the iPhone you won't get newsprint on your fingers either. There has been a host of these games released. To come up with a number, taking into account the thousands of games released for the device, is almost too daunting to consider.