Now, you can use AppManager to backup most apps, but protected apps are not included in this because they are stored in a different directory. With a rooted phone, you can access this directory and copy the apps to your SD card or to your computer. 

First method, copy with your phone to SD card:

  1. Install and open a Terminal Emulator on your phone.
  2. Enter su to be superuser (root).
  3. Enter cd /data/app-private/ to enter the protected application directory.
  4. Use ls to view the apps in the directory.
  5. Enter cp filename.apk /sdcard to copy a single app to your SD card.
    (Or to backup all the protected apps: cp * /sdcard)
  6. If you want to backup all your apps, they can be found in /data/app/

Second method is to use Android Debug Bridge with your PC:

  1. Install the Android SDK on your PC
  2. Connect your phone to your computer via USB cable, and make sure USB debugging is enabled on your phone (Settings > Applications > Development)
  3. Enter adb shell to fire up Debug Bridge and enter shell mode
  4. Enter su to become superuser
  5. Enter cat /data/app-private/filename.apk > /sdcard/filename.apk to copy the file to the SD card.
  6. exit
  7. exit
  8. And finally adb pull /sdcard/filename.apk filename.apk pulls the .apk file from your SD card to your computer.

Success? Problems? Moral issues with copying software? Let us know in the comments.