What is the best way to destroy data on unused parts of my HDD?

I’d like to overwrite empty space on my hard drive with zeros, or do whatever it is that one does to permenantly destroy old data on now-empty space there. What is the best (free) program to do that? Can I be assured that in doing so, I’m not going to bugger my computer and have to wipe my drive and reinstall everything?

Try Eraser (Windows only).