Wrt Rogain's original question:

Decide what you are looking for: File backup or disaster backup.
Then, solutions will depend on your OS/platform.
I have tried many PC and a few Mac disaster recovery solutions. Several look good until you really need them. Only 1 way to know: test the disaster recovery performance. (My criterion: If your computer was lost and you buy a similar/newer replacement, will the program get you up and running in 1-3 hours with all of your data and programs.)
Disaster backup: For the Mac, Time Machine is very good. Even better is to clone you disk using the Mac utility "disk utility" to intermittently create full disaster recovery (bootable) backups to USB-attached HDD. You MUST boot the Mac from a boot DVD (or USB drive if a Mac Air) to write a complete and reliable disk clone.

File backup: Currently I use DropBox. All important files are in folders under DropBox, and are mirrored to another computer and the DropBox website whenever I am internet-connected. It is hard to get far behind on file backups with DropBox or equivalent. The key features that determines usability for file backup are 1) must sync to a server or a always-available mirror machine, 2) run automatically in the background. A big plus is iPhone access to my DropBox files. (I pay for extra DropBox space.)