I have used AppBackup for several years now for specifically this reason. Not all games support iCloud and then you could use iTunes to backup your device but I've lost game saves this way in the past. It's been a really long time since I've tried using iTunes for this. Maybe it has gotten better. I have always just used AppBackup because I have NEVER once run into problems with it. It backs up all your App Store app data including game saves. I have game saves from when I first got my 3GS and they're now on my 4S lol. Would you like a step by step tutorial on how to use AppBackup? After using it, you need to copy a folder from your iDevice to your computer. Then after you restore and re-jailbreak you copy that folder back to your iDevice, install AppBackup and whatever games you want to restore, and use the app to restore all your App Store app data. Don't worry though, because whatever games you don't install, the game saves for that non-installed game are still on the device in the folder you copied to your iDevice. So you can save space on your iDevice until you want to play the game. Then whenever you get around to installing it, then it will appear in the list of apps in AppBackup. Does that make sense?
It takes maybe 5 mins in all to do this whole process. The time consuming part is restoring, jailbreaking, and putting all your stuff back onto the iDevice like music, apps, contacts, etc. Let me know if you want a tutorial or you need help. I use it ALL the time. AppBackup is always on my phone and I randomly backup my game saves just to be safe. Super easy and worth it. Plus its free. There are some other programs that do this too but I've always used AppBackup.