Welcome to Android Central! I assume you have the Droid X, although there was also a Droid X2. mumfoau is right, it could be rebooting on its own at night--the next time you hear it happen, turn on the phone to see if it's on the bootup screen (the Droid robot eye). But the other possibility is that one of your notifications is set to the "Droid" sound. You can figure out which app by, again, turning on the phone the next time you hear it, and (if it isn't rebooting) look at the notifications to see what app just gave you a notification. Then open that app, go to its settings menu, and look at the notifications option. Make sure it isn't the Droid sound.