Just to add my voice to the discussion, I've had my HTC Incredible since launch. Up to about a month ago, it was working perfectly. Last month I was travelling to Tampa, Florida and while accessing some news feeds on the Verizon network (no wi-fi available), the phone spontaneously rebooted. It continued to do this until it finally got stuck on the white HTC Incredible screen. I removed the battery and was finally able to get it to stay on, but for the rest of the trip, this continued to happen. When I got home, I did a factory reset and also formatted my sd card.
Since then, I've had various similar episodes. The one constant has been that I've always been on the Verizon network when the rebooting begins. As far as I can tell, it's never happened while on wi-fi.
While at lunch today, the rebooting began again while reading my twitter feed. Again, there was no wi-fi. While I was at the same location, I could not get the phone to stay on. It continuously rebooted, but as soon as I was back in the office, the phone stayed on and is working fine. Only difference is that it's on wi-fi now.
I just called Verizon, and spoke to Tier 2 support. I explained everything that has happened, and they are shipping me a refurbished unit tomorrow under warranty.
I apologize for my long-winded first post, but I thought it may be helpful to someone.