Since Dropbox has implemented an API, quite a few application already use Dropbox to synchronize its content (whether it be documents, game stats or whatelse).

However, still not enough developer use it.

Dropbox has released an API for different languages.
What would be, if someone made an app, where you can select apps (e.g. Angry Birds) and the content of its "Documents" folder get synched to a dropbox folder.

Now when you select the same app on another iPhone/iPod/iPad the content will get synced back and thus the game data is in sync.