My PC has two internal 120GB hard disks, the second one being dedicated to recording TV programmes, and to have enough free space for this purpose it cannot be used for backups. So I use an external USB2 120GB hard disk for backups. This solution works, but is extremely unreliable, often giving "Delayed Write Failures." Anyway, this is a whole other issue, but if you're interested, you can read all about it here: http://www.hardwareanalysis.com/content/topic/2459/?o=0. In any case, I use InCD-formatted CD-RWs and DVD-RWs to backup data that changes often as another level of defence against data loss. For archiving data that doesn't change any more, I use CD-Rs.
Once upon a time, before hard disks were common, I backed up data on two floppy disks (5.25" ones). Unfortunately, both disks became corrupted at the same time. That was the last straw that turned me into a backup freak. That's why I do my backups often, and for important stuff, preferably on media that I can bring offsite.