Any computer that leaves my possession (giving away, selling, whatever) has the hard drive removed and physically destroyed (after a DBAN run). I mean I really go to town on the damn thing. That is assuming, of course, that I can't use the old hard drive for something.
I'm pretty sure the only people with a chance in hell of getting any data off of the tiny slivers I leave behind would be in some alphabet soup agency (and even they would have a hell of a time). Since I have nothing that would interest them in any way, I don't worry too much about it and toss the confetti (that used to be a hard drive) into the trash).
If I'm donating the computer to someone or some group who can't put in their own hard drive, I'll buy a new, cheap one and put it in for them.
The only time I've ever violated this policy was when I had a HDD that was failing early in its lifespan: it would work for 20 mins at a time then fail. I wanted to send it in for warranty replacement but obviously wasn't thrilled since it contained data. The only content on the HDD was personal photos (nothing compromising) but I still am very paranoid about any kind of infosec. I kept the HDD extra cooled (even stuck it in the freezer at one point) so that it would stay alive long enough for me to do a multi-pass wipe on it. Even then I didn't feel great about sending it in.
Am I overly cautious? Probably. Paranoid? Maybe.
And yea, I try to be just as vigilant about back-ups. I slack off from time to time for brief periods, but then I kick myself in the butt. I'm not so great about backing up the state of my OS and its programs (although I will do a full disk image from time to time), but I'm pretty good about backing up my photos and other irreplaceable data.