This is a stupid question, but I just got an iPad mini for Christmas. I have an iPod touch, and want to sync my app data for my games, etc., across devices. Does this happen automatically through iCloud?
No - iCloud doesn't let you choose things to sync so the developer of each app you run needs to decide how and when to incorporate support for iCloud.
It's not such a silly question since I can't seem to find any Apple web page that explains this plainly.
As you find things that don't work with iCloud, you can pester the developer (kill them with praise and high marks even if you feel you want to give them a bad rating since you can expect them to please their fans first if they have any doubts about which tasks to add to their apps).