The scariest thing i've ever done with a comp was the second computer i ever built from new parts. (Athlon 800 tbird, 512 pc 133, etc) I had assembled the computer, set it up, tweaked it, and generally had it running fine. The only thing was it seemed to be running hot. I looked through some forums and figured that maybe i had too much thermal paste on it. without thinking, I took the heatsink off while the computer was still running. In about 3 seconds the onboard speaker started screaming at me and i realized the computer was still running. It probably ran for about 10 seconds without a heatsink before i could get the thing unplugged. I am still amazed that the system worked with no problems after I remounted the HSF.
I did fry my Radeon 8500LE when I was mounting a large aluminum cpu heatsink onto it. I was figuring out how it would fit best, when i accidentally scraped the pcb with the corner of the heatsink. That was the end of that card. I ran an old TNT Vanta LT for several months before i could afford another card.
I also fried a complete system (not my own 🙁 ) via static electricity (everything was fried, cpu, vidcard, etc) when i was assembling the comp on carpet. That was within a 2 weeks of when i almost fried the Athlon 800 above.
I've also seen smoke come out of several cheap power supplies.