As mentioned, you need to root your device to be able to make a full backup.
In addition to what
@Deletedmessiah said about doing a Nandroid backup which creates an image, you can also do a full backup of all your apps including their data and your phone's settings with Titanium Backup.
EXTREMELY powerful tool. Backup ALL apps, Market links, remove bloatware & MORE!
play.google.com
When I buy a new phone, or before installing new custom firmware on my phone, I use Titanium Backup to crate a backup of all my installed apps and their app data. I can then restore the backup on the new or updated device and will not only get back all the apps I was using previously, but any saved data from the apps too.