If you're using W2K or XP, check the Disk Management utility - you should be able to create a mirrored set without bothering with a RAID controller (unless you're building a high performance server that's going to be taking lots of disk traffic, you shouldn't need a seperate controller).
As far as "needing" a realtime mirror rather than an occassional CD backup - with how cheap hard drives have become, it doesn't have to be "need" of an RT mirror so much as being willing to pay a couple hundred bucks for added redundancy and not worrying about backups in the event of a HD problem.
CD backups are OK if you've got a comparatively small hard drive. But if you're using larger format drives - forget it. Even if you're using a DVD writer, it could take 10+ DVDs (or a whole lot more CDs) and a lot of time to backup (and later restore) a fairly full 120 GB hard drive - but with an active mirror, if the primary disk fails you can keep going and with little or no interruption instead of the alternative.
If you've ever had a disk fail on you and had to screw around with replacing and then restoring, a couple hundred bucks is cheap insurance to not have to do it again.