Is a random shut off a software or hardware problem?

One time while typing a txt in the stock sms app it rebooted.

Even weirder while plugged into a charger with headphones on yesterday it actuall shut off.. not rebooted, but simply shut off twice within 10 minutes while watching movie trailers on YouTube

Mine has rebooted about 5 times since I've had it, all while using the stock SMS app typing a message.
 
I've had 3 random reboots so far. The first time, I clicked a trusted link from within Gmail and the browser briefly opened up... the phone immediately rebooted. The 2nd time, I was listening to Spotify with headphones while the screen was off for a minute... then another reboot. The most recent occurrence was after I connected it to a charger and it was just sitting there... until it rebooted. It may just be a coincidence, but I was on WiFi every time.

After owning an HTC ThunderBolt since it's launch, I've experienced these exact same random reboots early on. A few software updates later, and they were completely eliminated. This appears to be less of the work from a "rogue app" and more of a voltage/radio/ICS software issue, needing attention from the powers that be (Google, Samsung, and Verizon). There's also been quite a few posts in the Google forums about this. Let's hope we can get an official word soon.
 
Only had my phone crash once. Mine was also after playing some notification tone. Haven't had issues before or since.
 
I too have been bothered by random reboots (about 8-10 since I got the phone December 15th). For me it happens about every other day and has happened most often while listening to Google Music. I had VZ Backup Assistant disabled but otherwise I'm running a stock phone. I enabled VZ Backup Assistant two days ago and I'm waiting to see if my phone reboots again. Perhaps that was a conflict?

Did any of you experiencing the same issue also have VZ Backup disabled?

Is it possible to look at a log file to determine what was happening just before the random reboot?