Just adding my experience to help others who come across this thread, I had the EXACT same experience of watching YouTube videos and then suddenly, they would stutter, then freeze, then the machine would spontaneously reboot. I disabled Flash and haven't had any reboots since. I do still have Hardware Acceleration enabled in Firefox though, and one thing that does still happen is that I get graphical glitches in the top left corner of the screen, which go away once I redraw the screen by minimizing or hiding Firefox and then bringing it back to the front. I haven't tested it yet, but I'm pretty sure that if I also diasabled hardware acceleration, the graphical glitches would disappear as well.
I want to emphasize that this is a Firefox specific issue, as none of the rebooting or graphical glitches occur in any other browser.
I also want to point out that since disabling Flash, I have run into very few videos that I could not play. Web sites are no longer as dependent on Flash for video playback as they used to be, and you can now disable it and not even notice that's it's gone.
So, to summarize, you can fix these problems in Firefox by:
1. Disabling Flash (Tools -> Add-ons -> Plugins -> Set "Shockwave Flash" to "Never Activate")
and/or
2. Turning Off Hardware Acceleration (Firefox -> Preferences - > Advanced -> General -> Deselect "Use hardware acceleration when available")