Which parts would still be useful for other pc's in your home? RAM? Graphic card that came with the computer?
Hard Disk Drive, I would presume. For additional storage, not speed though. Old RAM would be much slower (DDR3 > DDR2 > DDR) than new RAM, and is probably much smaller in capacity. Graphics Card. An old graphics card? I guess depends on your card then. Fans. Those should work okay.
Seconded on the harddrive. Through that baby in an enclosure and BAM there you go. I'd say hang on to the gfx card to, in case your current one dies a horrible death. You'll at least be able to use the computer to buy a new one.
The story is that my moms old computer got taken apart, and it has a better RAM and maybe graphic card than mine. Can I put it in without risk of explosion?