If a computer is powered off without being properly shutdown, can it hurt the hard drive?

YES!!!! During the shutdown process, not only is data being rewritten out of ram back to the drive, the drive is being told to spin down and seat (stop) itself. By cold powering off (like pulling the plug out of the wall) the drive does not get the opportunity to properly shut down. You risk data loss/corruption and/or forcefully causing physical damage to the drive. Remember it needs to slow down form maybe 7200 rpms to 0 rpms. Spinning all by itself down is like letting your car go down a mountain with out brakes and expect it to safely stop at the end. (Return to FAQ page)