In my recent review of the iPod nano (3rd-gen), I noted that the nano is compatible with iPod games from the iTunes Store. However, a slight clarification/correction for this statement is in order.
Apple has updated three of its iPod games (Tetris, Ms. Pac-Man, and Sudoku) so that they are now compatible with the third-gen iPod nano and the iPod classic, in addition to the iPod 5G. However, the remaining iPod games are still compatible with only the fifth-gen iPod; not even the iPod classic has been certified as being compatible with these games, at least for now.
Now here's the not-so-good part: if you previously purchased Tetris, Ms. Pac-Man, or Sudoku for your iPod 5G, and you would now like to obtain the updated versions of your games because you bought a third-gen nano or iPod classic, or you just want the bug-fixes, there does not appear to be any way to download the new versions short of repurchasing the games at full price. This is a pretty serious oversight that I hope Apple will address.
Apple still isn't offering any games for the iPhone or iPod touch, although they could still theoretically be introduced in the future. There are, of course, some web-based games that are compatible with Safari Mobile.