Just happened to me, had droid a few weeks. Removing battery (twice) finally did the trick and it re-booted. Not a charge problem -- was at about 90%
I did notice a few things... When I bought the phone the verizon store installed an "advanced app killer". Since getting the phone I've also downloaded over a dozen apps, some free, some a few dollars, all from the "app store". I noticed that no matter how many times I use the "app killer", the available memory kept shrinking slowly. Now that I removed the battery and rebooted the phone, I'm back to 117 available megs. I wonder if one or more of these apps or the phone OS itself has some memory leaks. Eventually, memory is consumed to a point where something breaks and the phone fails to run (even fully charged). Remove the battery, let it rest for a few seconds (drain the capacitor) and put it back...
This is pure speculation, but I do wonder... Will be tracking this issue carefully for a while to see if Motorola has a fix or even recognizes the problem.
thanks
matthew rapaport
quineatal@gmail.com