You should back up important files any time you take your computer in for repairs. For most people, the backup will be too big for a thumb drive or writable CD. External hard drives offer lots of space. And they stay with you while the computer's in the shop.
Hard drives are massive
You can get a roomy 80 GB external drive for around $100. That should be enough for important documents and multimedia. You may need a larger one for your entire drive. Prices vary widely, so shop around.
Backups don't have to be complex. For many, copying the My Documents folder and email to an external drive will do. My Documents contains the My Pictures and My Music folders, among others.