Yes, there are at least two ways. I used both successfully when I migrated to the new Nexus 7 only a few days ago.
Many games support saving to the cloud when you log in with your Google account. (There is usually an option for that in the game and once you are logged in there are no additional steps required.)
The 2nd option is to use the app "Helium Backup", it's free on Google Play and it doesn't require root. You need to install a small program on your PC to get it to work, though.