A few questions:

Will the phone charge at all? Droids are always on when charging. The light on the side should be lit up if the phone is charging, too. If it won't charge, try pulling the battery again and waiting 2-3 minutes before putting it back in.

Also- have you downloaded any apps? You might try uninstalling them (once the phone is up and running) and reinstalling them one at a time to see if it's one of the apps. Sometimes they aren't 2.0 compatible, and sometimes they don't play nice with the OS. It's just one of the pitfalls of open source- QC can be an issue, but at the same time it's not restrictive like Apple.

Note: There have been lemons that have been shipped. If it continues to shut down or reboot on you, or if it simply refuses to turn on again- exchange it for another. This is a new piece of hardware and a relatively new OS. There are bound to be bugs.

 

Sorry- these crossed. Try dimming down your screen all the way (it's still pretty bright) and turning off your wifi and GPS. I have found that this has helped out a great deal w/ battery life. (That being said, I will be either getting an extended battery or carrying a second with me. I did this with my Samsung i760 so it's no big deal.)

I have also 'conditioned' my battery. After the first few days I allowed the phone to completely discharge and then re-charged it. I've done this twice so far and it has seemed to help.

Best of luck!

 

My droid is currently experiencing the same problem. I was using it about 3 hours ago and it had over half charge, but I took it out about 15 minutes ago and it's dead and won't turn on. I've had it on the charger for about 10 minutes but still getting no response. How would it drain so much battery so fast?

45 seconds after I posted this the droid powered back on but still... how did the battery die so fast?