This is from FoxKat who posted it in another thread...I felt it was worthy of a thread of its own...
Original post here... http://www.droidforums.net/forum/droid-razr-support/199998-process-system-not-responding.html
Power the phone off by holding the power button and choosing Power Off on the menu. Wait till it's completely powered off (the screen will go Black).
Now, hold power button and wait for the red M logo. Release power button and then sometime over the next few seconds or so, press and HOLD BOTH Volume up AND Volume down. Don't let go until you see the Lock Screen (about 45 seconds or so).
You will now be in Safe Mode. If the phone is successful in remaining booted and doesn't fail like above, I would point to an app you've installed as the culpret. If it fails while in Safe Mode, then you have a corrupted OS installation. Report back with your results.
Original post here... http://www.droidforums.net/forum/droid-razr-support/199998-process-system-not-responding.html