I've had mine since mid-February (62 days) and it has randomly rebooted 39 times since then. Sometimes it can go a few days without a reboot (April 3 to April 7, for instance), and sometimes it reboots several times in one day (March 26, March 28, and March 30 - it reboot 4 times on each day). It started rebooting right away - before I downloaded any new apps, but I was updating the apps that it came with. I initially thought maybe that's what was causing the reboots.
I've never used the camera, so that isn't what causes my reboots. The first third party app that I installed was Reboot Logger (which is how I know my reboot stats).
At first I was very concerned about the reboots, and I held off installing anything (except Reboot Logger), while I tried to determine if this was something that I'd have to return the device for. It seemed to be a common problem, and it was not clear that BestBuy could give me another one that would not also do the reboot thing, so I just decided to keep it. In the end, most of the reboots happen when I am not using the device, so I'm not really bothered by it. It is just strange.
I just want to add that I really love the nexus 7. It is just the right size and I enjoy all the things I can do with it. I wish the power button was a little further away from the volume button because I frequently turn it off when I mean to be turning it up, but that, not the reboots, is really my main complaint.