I installed a very ancient AMD CPU, I don't remember the exact details, but I was able to insert it the wrong way. It could run comfortably for half an hour or so with no heatsink (shows you how old it was) so I hadn't put one on yet as I was just testing.
Powered up the machine and a small puff of smoke came up off the processor! I actually watched smoke appear out of nowhere from the CPU. After I got my courage back I put it the right way, powered up, and that machine went on to serve files on my network for over a year until I replaced it. I guess I'll never know what broke.