A few months ago on the Arqade site I asked if the iOS version of Chrono Trigger put save games in the cloud. DCol provided a great answer detailing how to check if iOS apps you own backup to the cloud:
To check for other games/apps (if you own them) look under Settings > iCloud > Storage & Backup > Manage Storage.
The apps listed under 'Documents & Data' sync between devices.
The apps listed under your device's name are backed up, but not synced via iCloud unless they are also in the previously mentioned list.
Some games/apps sync using cloud servers other than iCloud (Eg: Dropbox). In this case, they would appear in the back-up list, but not the Documents & Data list, but would still be syncing.
While his answer is still the best one given the question I asked I was about to ask a similar question concerning another game. Obviously this won't scale. Is there a way in the app store to determine if an app (game) is iCloud (or other sync service) compatible before purchase?