I don't think I've had any major parts fail except when it's my fault. Usually I just haven't connected something right, though I have had the occasional bad stick of RAM, a couple of hard drives die (always with enough warning for me to back them up, thank god) and I could never get the front USB ports on my old case to work. But again, it's almost always that I've done something wrong (that or a software problem) and can easily rectify it once I figure out what it is.
I remember the first time I got a video card that actually required separate plugs from the power supply. I didn't realize that, so when I tried to boot it it made this continuous horrible high pitched scream. That was really stressful until I figured out what the problem was.