To add my experience:
My SGS2 runs Android 2.3.4, kernel 184.108.40.206, GINGERBREAD XWKI4). I've had it for just under a year and it has always run the stock Samsung ROM. My phone's not rooted. I've never had any trouble of the kind I'm about to discuss so far.
Today my phone has begun to restart when I power if off. Googled around, saw some people had such problems because of SD card problems. I unmounted the card, removed it, put the battery back in (yes the phone boot up on its own when I inserted the battery). Same problem with no SD in.
I then saw a thread that some people had the phone on the charger when trying to power off (or the phone showed being on the charger when it wasn't - thunder on battery level); my phone shows no thunder and it's not on the charger.
My 8-year old son has taken the phone for a spin today (which means he fires off about a dozen apps aftes he tires of taking pictures and Cutting the Rope).
Any thoughts about how I might go about diagnosing this? Besides rooting my phone, taking a Titaium backup and hard resetting?