I was just about to post this same question, but I also want to know how to restore the free apps I have gotten from the Amazon app store. Has anyone tried backing these up since they are not from the market will it back up like normal apps?
Sounds like MyBackup is the app for everyone here,,,
https://market.android.com/details?id=com.rerware.android.MyBackupPro&feature=search_result
The #1 backup application for Android. Secure your data with MyBackup Pro.
RESTART YOUR PHONE AFTER UPDATING
Supports All Android Mobile Devices and Phones:
HTC, Motorola, Samsung, LG, etc...
Backup (with schedule option) to our online secure servers, or SD card, your Applications, Photos, Contacts, Call log, Browser Bookmarks, SMS (text messages), MMS, Calendar, System Settings, Home Screens (including shortcut positions), Alarms, Dictionary, Music Playlists, and more...
Restore your backups on your existing or new phone.
View your data and application backups online, by logging into the Web Viewer at
RerWare, LLC: Android Backup and BlackBerry Backup - MyBackup Pro
MyBackup Pro will work on all Android mobile devices, regardless if they have root access or not.
Users who have a rooted phone: You can backup apk+data as well as market links!
RerWare, LLC: Android Backup and BlackBerry Backup - MyBackup Pro