How much games does a iPod touch get?

Do you mean 1) default games, or 2) maximum capacity?

1) The iPod Touch, unlike previous iPods, does not get default games. You must go to the App Store (Wi-Fi connection required) and download games of your choice.

2) The maximum capacity depends on how much hard drive space your iPod comes with. You can view how much space is free by going into Settings>General>About and scrolling down. Note that downloading too many apps (especially ones that run in the background) may slow down your RAM (128MB on 3rd Generation iPod Touches).