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!