Here’s an excellent, concicse blogpost that outlines both how identity thieves can scrape sensitive information from your discarded computer and simple steps you can take to make it harder for them to do so.

Stealing someone’s identity doesn’t take a lot of intelligence or even a lot of effort. The bad guys only need you to trust them with your hard drive and a combination of bootable live disks [to] turn your financial and personal life into a living hell.

I use Boot And Nuke to scrub my old hard drives, then I drill physical holes in the overwritten disks.