My wife and I have Droid2, not the global but we both have random restarts. My wife more than myself. I have owned the phone for 3 weeks and have had 2 restarts. Try a battery pull and restart on your phone and see if that eliminates it. Also pay attention to any apps you have installed to see if they are the problem. I would say if you are getting them frequently despite doing the above, to take the phone back and get it looked at or replaced.
I did not have any unwarranted reboots with my D2. Best guess is the hardware might not be up to spec (in which case Verizon would need to replace your device) or it's because of an app. Try uninstalling apps one at a time to see if that's the culprit.
I had my D2G for less than a day. We got two of them and the other one was fine, but mine did one random reboot and then just stuck on the Moto screen. Tried batt pull and hard reset. Tech said to send it back. Not very encouraged with this device...
I had many random restarts on my first D2G, got where it was doing it even in the middle of phone calls. I did battery pulls, factory reset, got rid of apps, etc. Nothing helped. I called Verizon and got a replacement one, and have not had an issue at all on the new one.