How do I undelete an app without losing data? My little sister accidentally deleted one of my iPhone games. I know I can get it back by "rebuying" or resynching it via iTunes, but this will give me a clean install, without all my saved game state. Is there any way for me to reverse the deletion without losing all this information?
You can restore from your last backup that contained the game, however you will lose any new additions you've made on the phone since the backup. iTunes normally makes a backup every few syncs or days, depending on how often you have plugged it in.

I would first try and just re-install the game since she may have removed the game but not the actual data associated to it.

Apart from that there is no way to recover the data, since the iPhone does an immediate delete of all files once instructed to do so.