Don't get caught with your pants down when your hard drive dies or you accidentally delete something. Backup up your data on a regular basis.
I can't tell you how many times I have seen a hard drive die and the person did not have a backup. Years of family photos and important documents completely gone. That is unless you want to send your hard drive to a professional restoration place and pay a couple thousand dollars to get it back.
So here are your options.
CD-RW or DVD-R/+R
If you do not have one get one. You can get a CD-RW drive for under $25 (watch your local paper or try NewEgg). Then buy a 50 pack of CD-R media, which are also very cheap if not free after rebates. Put the CD-R media in the drive. Fire up the software that came with the drive and run through the wizard to backup your data. Don't bother backing up programs. 99% of the time you have to have the installation CD's to reinstall. Just backup your data. Most software allows you to save the backup job for future use (kind of like a word document). All you have to do is open up the saved job and run it again with a new disk.
You can get about 700MB of info on a CD-R disk and about 8GB of data on a double-layer DVD burner. The new Blue-Ray DVD's can store up to 60GB and the HD-DVD about 50GB max.
From my experience CD-RW media is really hit and miss. Yes it does work, but I have seen a number of instance where it just does not. I have also seen where a disk that you create in one drive will not work in another. In my opinion CD-R is a much safer road to travel.
Another Hard Drive
Another quick solution is a second hard drive. Putting one inside your computer is the cheapest option, but more technical to get setup. A quicker solution is to buy or build and external unit that connects to your computer via USB or Firewire. There is a lot of great external hard drives that you can buy. I personally like the Maxtor One-Touch units. If you are a little adventurous and would like to save a few dollars, you can build your own external unit cheaper than buying one prepackaged. I know for a fact that CompUSA sells the empty enclosures then all you have do to is pick the hard drive you want to put in it. It is very easy to do. To save money on the enclosure just get the connector type you will really use (USB or Firewire).
Most external drives come with all the software you need. If you decide to go the internal route or build your own external unit, I recommend FileBack PC. It only costs $25 and you can set it to backup multiple copies of the same file over time all in the background. It is kind of cool because you can go back to a previous version of a file.
Online Service
This is a neat option because you can automate it and access the files from anywhere. Basically what happens is you install some software (provided by the service) on your computer and tell it what to backup. It then securely copies those files to the online service into your account.
The ones I am aware of and have tried are StreamLoad (free 25GB space) or Data Deposit Box who charges $2 per gigabyte per month. Either is a great deal. The nice thing about Data Deposit Box is the software completely automates the backup process. If you have a lot of music or photos (static content) you want to backup StreamLoad may be cheaper option.
Another FREE service is Xdrive . They give you 5GB of space, but with their client software you will see an X: drive added in Windows Explorer, which makes it very easy to understand and use. They also have automatic backup capabilities like Data Deposit Box.