Time Machine. (Mac-only.) It's free, it's built in to your Mac OS X software, so use it. You just need to get an external drive and hook it up to your Mac. You can get external hard drives cheap at places like Amazon. For example, here's a 1TB (terabyte) drive for just $99.
In addition to Time Machine, here are a couple of "cloud-based" services that I use to backup some files via the internet:
DropBox. This is a really nice little program you install on your computer. Basically it creates a special folder on your computer. Anything you "drop" into this folder gets uploaded and synchronized to your account. You can even have a "public" folder in there that allows you to share files with anyone — especially nice for files too large to send via email (you can just email someone the link). When you sign up, you get 2GB for free forever. But if you sign up here with this link, you'll get an extra 250MB of free storage. That's a pretty decent amount that allows you to keep your active documents backed up painlessly. You can pay for more storage, but I have found ~2GB to be more than sufficient. Another great thing is that you can access your files via the web from any computer if you need to, and they have versions for iPhone, iPad, Android, PC, etc.
Mozy. This is sort of like Time Machine, but it backs up your files to their servers. It's a free download for Mac or PC. Like DropBox, you can get 2GB of storage for free. But if you use this link, you will get an extra 250MB free. You can select which folders or files to back up. They also have an Unlimited Service for $55 a year that allows you to back up as much as you want. I actually subscribe to this service for my MacBook Pro — I was too lazy too connect to my external drive on a regular basis. So I have 57GB backed up via Mozy (my entire hard drive) — it took 7 days to complete, but now if my MacBook Pro is stolen or lost, I can recover everything.
Note: With DropBox and Mozy, the first time you backup might take a while (depending on how much you are backing up). After that, it will go much faster.