I had problems with my phone's camera lens cover so called customer service and they offered a replacement. Here is when I began having similar reboot problems that everyone else here seems to have. I agree with WarnerYoung that this issue is not always caused by apps.
The certified like new replacement boots up fine. I go to start activating my device and then the phone goes into a constant reboot cycle. Sometimes it would get to the lock screen, other times it would only get to the initial white screen that says "HTC Incredible". There was no way to turn the phone off (or stop the cycle) except to bull the battery.
So I called Verizon, they asked me to pull the battery out for a few minutes and try again. I do this, and again it looks like it is working fine, but a few minutes later as I try to activate it, the phone goes into another reboot loop. They are not sure what is wrong and send out another replacement.
My second replacement activated fine, and everything seemed to be going okay. Content with this replacement, I pack up my two other phones, my original and the first replacement, and send them back to Verizon. I come home, start setting up my phone. Everything goes okay for a little while, but soon my device starts restarting. At this point I had not installed any apps. I call up Verizon again, spend half an hour while the representative "researches" the problem. She has me try a few things to get out of the boot cycle. Nothing works so she sends me over to tech support who sends me out another replacement device.
After getting off the phone with VZW, I pull out my battery for 5-10 minutes, put the battery back in, and again I can get the phone to boot fine. Now if I don't do anything it seems that my phone stays booted and can receive calls, but as soon as I get on the web for a few minutes, the boot cycle begins once again. Sometimes I am even able to get a call out. I suppose I will just have to wait for the replacement device.
At this point I wish I just put up with my pushed in camera lens. It was solid and I never had a reboot issue in months (not even non-cycling reboots). I'm now onto my third replacement in the past week, and fourth overall (my very first device had to be replaced after having 3g radio problems a few months ago).
Sorry bout the long post but just thought I'd let everyone know that there are other people who are facing similar problems. From personal experience (my first and second incredible), I know that there are devices out there that do not have this issue. Hopefully I will get lucky with this fourth one and everything will work out.