When it comes to computers, it's not a matter of "if" you will have a hardware failure, but "when" you will have a failure. Eventually, you will have some bit of computer badness that could result in file loss. Unless you have a backup of course. Keeping your files organized not only makes them easier to find, it also makes it easier to back up your system.
If all your data is in one folder or set of folders, it's easy to copy them off to a CD or DVD. For example, I have backups of my client files. Many times I have had clients call me up asking for files that I created years before, which they have subsequently lost. Thanks to backups, I've always been able to say, "yes, I still have that file."
Many backup options exist today. In the past, I used dedicated backup software and backed up my data to tape. However, now most computers come with CD-RW and/or rewritable DVD drives. It's easy to just back up to those mediums using standard CD/DVD software that comes with your computer or even the copy facility that's built into Windows XP.
If you want to back up a bunch of photos for example, all you have to do is select them (or their folder) and drag them to the CD drive icon. It's easy. Of course, before you delete anything off your hard disk, be very sure to check your backup first. Sometimes CD writing doesn't work. If you have the option, take the disk over to another computer and check to make sure it's burned correctly and can be read on another machine.
If you have important data, you should have multiple copies of your backups that are stored in more than one place. Realistically, every type of backup media can go bad, and buildings flood, burn down, and so forth. Sure it's depressing to think about, but it could happen. So if you have an office, store backups at the office and at home, so they are in two different places.
Another option is to backup your data using one of the online services. I haven't tried this because it's somewhat expensive. Plus, you absolutely must have a really good broadband connection for it to be feasible. But it's definitely a viable off-site storage option and it can be set to run automatically.
If you travel a lot, little USB "thumb" drives are a great way to keep critical data with you. However if you opt to carry really important data with you like passwords, be sure to encrypt the data, in case you lose the drive.
The key to backing up is to devise a plan and then stick with it. For example, I have an automatic backup that mirrors one hard disk onto another. I also have an external hard disk where I can store "overflow" backups. Then I have CDs and DVDs stored off-site.