How old is the computer? If it isn't ancient, donate it to a local charity, particularly one that helps people get back into the workspace. Be sure to reformat the hard drive to remove the old data.
About reformatting:
You need to do this a lot. It's recommended that you do it at least 6 times. But there's software out there that can recover information even if you reformat a dozen times. They probably won't be able to get everything, but if people get the right bit of info - like your bank account number - then it doesn't matter that that's all they got. There are programs available that will overwrite your data to make it more difficult to recover. I've heard of a few but can only remember one called Eraser. Don't know if it's any good.
And don't believe all that stuff about putting magnets on it. There's a magnet in the hard drive that makes it work. You'd have to have a really big strong magnet to mess up a drive.