Android - Back up not only games, but also game progress before flashing ROMS

The best are backup methods that backup and restore app data. Titanium Backup is excellent for this, and easy to do, especially with the pro version. It allows you to backup the apps, including the relevant app data, which holds the game progress. The pro version lets you restore them seamlessly, while the free version requires manual re-install, like Astro. You can also sync these backups to online storage spaces like dropbox or Google Drive.

If you have multiple devices (I have a tablet and phone that I like to sync progress on, for example), DataSync is by far the best option. It can sync to dropbox or strictly device-to-device, but can sync all the app data with game progress to another device for subsequent use, or resyncing back to the original device later.

Let us know what you choose!

Another fool-proof method (no need to worry about having a specific backup app) is to grab the game's data directly.

The data for all user-installed apps can be found in /data/data/*package name*. This will be all settings, saves, and anything else. Just browse into there and copy the relevant directories to somewhere safe and put them back when you're done flashing and have reinstalled the app and run it at least once.

Yet another way, which will work without root, is you do the same as above, but using adb. Turn on USB debugging, connect up to your computer, and run adb pull /data/data/*package name* C:\where\you\want\the\files.

Then once you're done with your ROM flashing and have reinstalled the apps, do adb push C:\where\you\put\the\files /data/data/*package name*, or if you now have root with your custom ROM, just copy the directories you pulled to the SD card and put them back in /data/data on the device.

Give a try to Go Backup Pro which is completely free. It need root access and backup your apps+data, and when you will restore your backup it will not ask you Install app every time.

Backup contacts,messages,GO launcher settings, system setting and apps
Backup apps data（needs ROOT）
Hide annoying app installation interface when restore apps（needs ROOT)
Cloud Backup supported, sync to Dropbox.