Stock iOS devices have a leg up on Stock Android devices when it comes to backups. With iTunes you can create a full backup, and store it on your computer. It even does this automatically. Stock Android who has no way to do this. Once rooted however, there are several methods. The first is an App and Data only backup that requires root access.
Titanium Backup is an application that allows you to backup all of your apps, both on internal memory and your SD card, plus user data for those apps.
It is free, and you can get it in the market. There is, however, a paid version that allows you to do alittle more.
The app requires BusyBox, so search the market for that and install it for your device. Then you are ready to open the app.
There are three tabs on the top, but the one you will use the most is probably Backup/Restore. You will see all of your apps listed.
You can choose one by one the apps to backup or by tapping Menu>Batch you can see a list of commands to do a bunch at a time.
In the schedules tab you can also set times when you would like to do backups. For example i have a backup that runs every night at 5:00.
All of the backups are stored on your SD Card, so it is fairly simple to get them off. Just mount you SD Card and drag the titanuim backup folder to your desktop.
The premium version features better support and more batch operations. It can be purchased for 5.99 USD.
These backups are different, more simmalar to itunes backups. They backup EVERYTHING! When you restore it will be exactly the same as when you backed up.
First you want to open the market and install "ROM Manager" There is a free and paid version, although I HIGHLY suggest the paid version. Once installed your ready to start backing up. The easiest way is to open the app and tap "Reboot into Recovery"
If you are not automatically taken to the screen below, then use the volume buttons and select recovery.
If you want to backup, select backup and restore select restore. When you backup or restore an image like the one below will appear:
Once finished your phone will reboot. All of your backup files are saved on your SD Card in the /nandroid directory. You can then copy the backups to your computer.