|When you say "getting rid of my desktop" do you mean you are scrapping it?|
In which case take out the hard drive(s) and smash them to pieces.
If you are giving it away or selling it with a working operating system then you can simply go through the file system, block deleting all your own stuff. Afterwards use a free program like Eraser to rub out all the empty areas. They might still be able to retrieve some previously overwritten files if they are smart enough.
Always pop back and let us know the outcome - thanks