Yep, been having the same issue. Since I've had the phone on Thursday, I've had to charge it 2 times a day it seems. I upgraded from an LG Chocolate 3 because I wanted a new smart phone. Never had this issue with the chocolate 3, with heavy use I was able to charge it every 3 days. I'm not expecting that with a smart phone but every day and a half would be nice instead of twice a day. Of course, I was very very reluctant because I have had nothing but bad luck with Motorola phones in the past holding their charge... this one seems no different.
Just last night, I had given it a full charge to 100% (and maybe left it charging a couple more hours after that) after it drained battery completely. I went to sleep, didn't use the phone at all and whatta ya know... in 8 hours, it drained down to 30%.
Looking at this, I have my GPS off... my WiFi is also off because it continues to search for signal in spots that don't have wifi, so I imagine this kills the battery, the screen brightness is off auto and turned down (I would say to 15% or so), I have no live wallpaper being used just a normal one and the Facebook app was updated, due to a bug I read about on here and all this stuff still happened.
After doing all this, I had come down to two more possible culprits. I have a widget that was giving me live score updates for my favorite teams from ESPN. Not sure if this was causing a problem, but my friend uses it for his Droid X and has no issues (His gf also got the Droid 2 and she is having no battery issues).
I also found, under Data Delivery, an option that says "Background Data" and when I chose that, it popped up saying that shutting it off extends battery life and lowers data use and that some applications may still use the background data connection. So, I am shutting this off to see if this makes any improvements and will let the phone die out, again, and will give it a full charge and see what happens and will report back here later