I don't know if this one was already mentioned but I didn't have time to go through the full list of requests.
SyncBack is a full featured, easy yet powerful backup and synchronization utility.
It's already completely free and quite small so integrating it as a portable app should be fairly easy.
For more info on syncback visit:
http://www.snapfiles.com/get/Syncback.html
Check out my Synkron Portable development test release, or Toucan.
The developer formerly known as ZGitRDun8705
It's not completely free, theres a pro version of it. But yeah, probably the best of it's class.
Last time I checked it writes to 'C:\Documents and Settings\[username]\Local Settings\Application Data\2BrightSparks\SyncBack' , I think the pro version only writes to the registry for license key.
What about the NO INSTALL zip on their forum?
http://www.2brightsparks.com/help/index.php?action=kb&article=233