I have a iPhone 4 can I be on my games when I don't have internet?

[Daniel]

Most of the games on your phone will be available to play offline, such as Temple Run 2, unless there is some kind of multiplayer element to it (online multiplayer game / MMO). Other applications such as Facebook and Pandora Radio require a constant internet connection to use them, although they will still load without the internet. Downloading apps or buying content from inside an app requires an internet connection.
If your phone connects you to 3G automatically, then there should be an option to turn it off somewhere in the Settings so that you don't accidentally use it when you don't want to.