Hmmm, as a person who loves tinkering with "used" stuff, I'm a bit conflicted about how to answer this.
In a system that "really" matters to me, about the only used components will be a floppy, CD-Rom (but probably not, since you can't even really get a good deal on the used ones compared to a new one) and possibly a harddrive that's serving as a backup.
I'm really surprised more posters haven't said motherboards/processors/cards, because of all the used stuff you could get, these are most prone to being damaged in subtle ways, i.e. electrostatic discharge that doesn't cause a component to fail completely, just causes it to do "weird" stuff. I used to believe that if an electronic component worked for an hour, it was 100% okay. After a few years of building systems from used parts and coming across problems that were inexplicable even to hardware gurus, I am now convinced that that belief is very mistaken.
Get your hands on some damaged but still functioning memory and plug it in your system, and watch the kinds of bugs that start popping up sporadically. It can look like ten million different other things to do with your OS. You can pull your hair out for weeks.
I still put together "used" systems, but only when it's a situation where I can play with it at my leisure, swapping components in and out, and not a situation where someone wants it to work perfectly NOW.