For as long as you are alive? Well, unless you aren't planning on living too long, I'd remove the "spending a fortune" from your thoughts. I do a fair amount of backup for financial organisations, and believe me, even guaranteeing data for 10-15 years is a pain...
If you want it "secure" - by which I think you really mean "recoverable" - than a minimum of two copies, both stored away from the original machine is a must. Normal procedure is one copy on external disk, another on tape; and both taken "offsite" in case of theft or fire at the original machine's location. Oh, and don't forget to do regular recovery tests on these backups, just to make sure they actually work come the day you need them...
On the other hand, if you just want something "cheap", do as some others have suggested and get an external drive. Go eSata if you can, or you'll just end up choking on bandwidth. A proper backup program that can do "incremental" backups will help massively here. Many external hard drives come with such software, so shop around. Also, don't forget to take take the external drive/tape and store it someplace else, in case of fire, flood and/or theft.
And also remember to take multiple backups, not just one. If you delete some stuff (or files become corrupt) and then go an make fresh backups over your previous backups , you'd be screwed; multiple backup copies from different dates gets around this problem.
Now you can understand why backup systems are so expensive!
Nomadd