Throwing your hard disks away is a major, major security risk. There's a lot of sensitive data stored on your hard drive that builds up over the years. Even deleting the contents or formatting the old drive isn't enough - people can (and do) recover 'deleted' information all the time. Just search for "recover windows files" in google to find the millions of matches on how to do this (yep, there's legitimate reasons for doing this - like when you've deleted a file and need to get it back!)
The best way to make sure your private information stays safe is to wipe the hard disk before throwing it in the trash. There's a number of free tools out there to do this. If you're running Windows then a great utility is Disk Wipe.
It's a free download and very, very easy to use. After installing you just run the program and select the drive you want to wipe. Be very, very careful and make sure you select the right drive, there's no way to get this data back once it's wiped. Also make sure you've backed up everything you need before doing this - there ain't no turning back!
The next option to select is the level of wipe you want to do. The option at the top is both the fastest wipe and least secure, the option at the bottom is the slowest wipe and most secure. Typically I select one of the options in the middle - it's a good tradeoff between speed and security. If you're paranoid, select the bottom option and come back in a day - it takes a while!