vehelpfulguy - hard drives are less likely to explode than a CD or DVD is to get scratched. For a basic bit of home PC backing up, a reasonable Hard drive is the way to go (although DO avoid very cheap ones!)
For more serious back-ups, you'll want to back it up to 2 separate devices.
For crazy back-ups, you'll want to back it up to 2 devices and take one off-site and also have a RAID Mirror set up on your PC.
But this guy is just running out of space and so buying more space seems the most sensible answer imho. Slap it into the USB port, drag and drop, job done.