Here's a great example of why you should physically remove and destroy your hard drive before trashing your computer:
Some folks will tell you that if you delete all your files or Format your hard drive it's safe to give it away or trash it. NOT so! Deleted files are easily recovered (especially if after they are deleted there is no additional activity on the drive). Even formatting the drive doesn't remove all traces of your data. There are lots of utilities (many of them used by computer forensic experts like those you can find at the FBI) that can restore date on a reformatted disk to readable condition. Hard to believe? Here's an example of software that will do the trick: http://www.recovermyfiles.com/
Bottom line: if you are going to trash your computer, open the case, remove the hard drive, and literally beat the crap out of it with a heavy ball peen hammer or small hand sledge. Then trash it.