General
A backup is a complete copy of your work.  This can be achieved via floppies, tape , recordable CD, DVD, USB memory sticks, or external hard disks.  There are online services that you can send all your data to, I've never used them but you might want to.  Just remember, they have your data.  Also, some applications can be set to make a backup copy of your work - as you work.  AutoCAD and MS Office can do this.  This can double your disk space usage, but can be a good idea.  This places a second copy of the file in the same folder.  Just remember, its on the same hard disk, so if it fails (or is stolen), you have no backup.

For my home network, I have moved solely to external hard disks.  CD's and DVD's are just not big enough.  It's also important that you have more than one media.  I've seen the results of lightning hitting a computer - the hard disk was toasted and the tape that was in the tape drive was usless.  You must make sure that your files are copied and then the media physically moved away from the computer, all on a regular basis.  The cost is much less if you use external hard disks for single computers (and small networks).  The only reason to use tape is if you must keep a large library of many different media and/or have many terabytes of storage, then the costs are lower.  This is due to the cost of most tape drives ($800 and up).  The general rule is: as more media are required (tape or disk rotation), it is cheaper to go to a tape solution.  There are low cost (sub $300) tape drives, but they are very flakey.  I used to use Colorado Backup with one of those cheap drives and I'll never do that again.  

I use two external hard disks for my home computers.  They are universal and need no special software.  Just find a computer with USB and plug it in, viola, there are your files.  I have been very pleased with the AMS Venus External Enclosure, much more so than the Bytecc brand.  Alternatively, you can use the disk drive manufactures products (Western Digital, Maxtor, Seagate, IBM etc).  They all make these with some bundled software, but I've never used them because they cost a lot more than what I can build.  Plus, the software doesn't do much more than what you can get for free.  On the other hand, most have a big fat button you press on the drive and the backup runs, you aren't going to build that feature (yet).  They are very easy to put together.  Go buy an enclosure and disk drive, open the enclosure, attach the drive, close the enclosure, you're done!  I have been very pleased with the speed of my USB 2.0 and Firewire (IEEE 1394) drives.  To achieve those speeds in a tape drive, you talking $3500 for the drive (and probably $50+ for the tapes).  Also, I would recommend firewire over USB 2.0, it has a slight advantage in that it is a little faster, but it has error correction (like a higher end tape drive).  

Operating System versus Data
These should be kept separate.  Why?  So they can be backed up separately.  They have different needs.  The OS and Apps change very little and should be relatively small (say no more than 10 GB).  Yes, I said 10GB for OS/Apps, our work computers have XP, MS Office, TWO AutoCAD installations, Corel Graphics suite, and numerous engineering software applications, all take up no more than 10GB.  Then we have the data which can be hundreds of GB, or more.  This can change a great deal and is ever-growing.

For home computers that have no network, I have been using one hard drive with two partitions.  One for Drive C: (at least 20GB) and one for Drive E: (all of the remainder). The C: drive contains the Operating System (Windows XP Pro) and any Applications (Microsoft Office, Adobe Photoshop, Norton Antivirus, etc...).  The E: drive contains My Documents and some manually created folders.  This enables the two to be backed up separately.  Also, it allows the OS and Applications (C: drive) to be imaged and then re-imaged.

Operating System and application backups
Since the OS and Apps are on the C: drive, we can use drive image technology to get an exact copy of it.  The important thing to note is that this usually involves booting to an different operating system (on CD or DVD) this renders Windows inactive.  I usually run a drive image of the C: drive before installing any updates or other software.  If the new software has problems, then I just restore the entire C: drive back to the way it was.  Windows XP System Restore lessens this need, but I this has saved my lunch a few times.

Drive Imaging
I really like using drive imaging technology.  It solves many problems with Windows based software.  I have used Power Quest Drive Image, Norton Ghost and now I am using Acronis True Image http://www.acronis.com exclusively.  It can support just about any device you use to make an image.  It can even run while Windows is active and get a valid image.  I have done this with a server and it worked beautifully.  Just don't make your drive a Dynamic Disk using Windows Disk Manager, keep it as a Basic Disk.

Data only backups
This is a backup of the data partition (E: drive) to some external media (disk, CD, DVD, etc).  You can run a full backup and then daily incrementals (changed files only).

External Hard Drives
You can build an external firewire or USB hard drive.  Or you can purchase a bundled external hard drive / software - I would lean towards anything from (first choice) Western Digital or (second choice) Maxtor.

Software
You can use the built-in NTBACKUP, it's easy and includes scheduling (but it does not compress or span media).  Or, if you want to get into scripting, use XXCOPY.  If you want an easy-to-browse database of all your backups, you'll need different software (get your wallet out), see the Small Business Networking section.  I've seen plenty of very low cost (sub $40) products that use a graphic interface to WinZIP.  I would not use zip technology for backup, zip is for temporary file transfer.  I've seen plenty of zip files be corrupt and not openable.  Not what you want for backup.  If you have an external drive, it may have come with some software, but you should be able to use NTBACKUP or XXCOPY.

Windows System State
NTBACKUP allows you to capture the System State.  This is a must to enable a full recovery in the event of a hardware failure.  Be sure to include this.  Of course, if you put Windows on a separate partition and ran a drive image, you'll have this.

Windows XP System Restore
Be sure to enable this, it can help recover from a bad patch or failed installation.  I've used this sparingly and the default settings seem to work fine.