Droid X Turns Itself on Automatically
I have the exact same problem. I have confirmed that my phone is powering off (I get the "powering off" message and then the screen goes blank). But some time in the night, my phone turns on by itself.

At first I thought that I was accidentally just setting it into the new (with Gingerbread) sleep mode. But I'm careful and I'm definitely pressing "power off".

Lots of people are reporting this same problem. Other forums have suggested changing the timing of the backup assistant. I've tried that, but to no avail. 

It seems clear that this is a new issue with Gingerbread.