I have a Dell Inspiron 1318 laptop, which is two years old. Recently, the battery finally gave up the ghost, so I've just been running it off the AC adapter. Every now and again, it just turns off. It turns back on fine though, no error messages other than the standard "You didn't turn your computer off properly etc etc" screen upon start up.
I'm positive it's not overheating, as I have a heat monitoring program called Core Temp installed and I'm careful to keep the computer as cool as possible, with no vents blocked and it's always on a hard surface.
I recently replaced the AC adapter as the old one was becoming ureliable. It's plugged into the wall, not a surge protector, and there hasn't been any thunderstorms lately, so I know nothing got fried.