I backup onto a large external hard drive. I just copy the files I want into a new folder named similar to backup-laptop-20090627 in an organized fashion.
Some external hard drives come with backup software that works on Windows, but I've never used any of them.
Also, CDs and DVDs are very good for permanent storage. Some people backup to DVDs and put them in a safety deposit box; this way your data is still accessible if your house burns down. Also, some paper-shredders come with CD shredders - look into this if you don't already have one.
If you have an additional internal hard drive, you can easily back-up to it. However there are many drawbacks to this. If you're computer fails (like if your CPU burns up), your data is not easily accessible. If an electrical surge manages to hit your computer, your data will be lost. If your house burns down, it won't be accessible, etc. But, this method is still good for intermediate backups.
Remember, relative to other components, hard drives are quite unreliable. Always try to have your data in more than one place.