I'm having a similar problem with my six month old Motorola Droid. I love my phone, and have found battery usage to be fine. I use the web access but don't play games or run a lot of apps. I plug the phone into the wall charger most nights, but generally get through the next day okay if I forget.
Recently, and with increasing frequency, I pick up the Droid during the day and find it turned off. The power button will not turn the phone back on. If I remove the battery, wait a moment and put it back in, the phone powers back up, and shows that the battery has plenty of charge left.
I actually had a similar problem with my Motorola Razor, which was an early model. I scoured the contacts and replaced the battery on that phone, and had some improvement.
Anybody know what's going on with the Droid, and how to handle it?
Thanks!