Update: Whoops. Koush sends word that Carbon wasn't quite ready to go when we posted and that the folks in the forums spotted it early. It's now "live" live, so make sure you have the most recent version.
After a couple of weeks in beta, Koushik Dutta -- aka Koush -- has released his Carbon backup app on Google Play. The app uses Android's built-in backup feature to sync apps -- and crucially, app data -- to the SD card or cloud storage. If you're rooted, you just need the app itself. If not, there's an accompanying desktop app that can help you sync an unrooted phone.
A word of warning for Motorola users -- the app isn't available for Moto devices due to a bug in these phones which prevents Android's backup features from working correctly. A manual download link is provided on the Play Store listing for those running custom ROMs, or anyone who just wants to try anyway.
Carbon comes in two flavors -- there's a free version, which offers an basic ad-supported service. Then there's an ad-free premium version, which costs $4.99 and adds in more advanced stuff like Android-to-Android sync and cloud storage sync.
Both apps are available for phones running Android 4.0 or above -- hit the Google Play link above to grab the basic version, or head over here for the premium version.