My experience is that any and every user appreciates the importance of backing up your stuff, but when it comes to actually doing it, almost nobody does it, and even some large organizations are failing at it. Backup failure isn't necessarily "not doing it at all", but can also mean that it's done improperly. A proper backup is such that a person or organization will never, under any circumstances, lose more than a day's worth of work. Before we even go there, I should stress one important fact - many users, and even experienced system engineers often confuse between backup and archive. Backup is when you copy your current data to another storage medium, so that if something happens to the original, you can restore it and not lose anything. Archiving is similar, but opposite - you copy your data to another storage medium, and then delete the original.
For example, many people burn DVDs with their older files and delete the originals, and most of them consider this a backup. This is, in fact, an archive, but few people are aware that a recordable DVD has a limited lifespan, and is very sensitive to physical harm. Putting your photos on a DVD and stowing it in the closet is not safer than storing food in the trunk of your car. Often, we discover this only in hind-site, when trying to recover a file from a disc burned 3 years ago, only to discover that it's partially or completely unreadable.
I believe network engineers won't need to read this, so I'm addressing this to the home user, mostly. For a backup to be worth anything, it has to meet some basic principles:
1) It has to be done to a media with at least SOME reliability.
2) It has to be done frequently.
3) It has to be stored in a place that is safe, but not too unreachable.
4) It has to be tested routinely.
What does all this mean? Well, 1st, this means you should not use a media that's unreliable. A writeable DVD, for example, has a low reliability rating, while a hard drive has more. That's not to say that a hard drive is bulletproof, but it's usually more reliable, and also easier to detect if it fails. This is because if it dies, you would usually be able to hear it, and respond by replacing it, while if a DVD stops being readable, you'll only find out when you put it in the drive. A high level tape drive, like an LTO or DLT is also very reliable, although these babies start at a few hundred dollars, so would be off the table even for some business customers.
A frequent backup is also important. Many users start this with full intentions of going all the way, but after a while, they kind'a give it up, and forget to backup for weeks or even months. Typically, you remember to do it right after your hard drive crashes, of course. A good way to avoid this pothole is to setup some automatic backup mechanism. If you use an external drive, for example, this can be done rather easily, and many external drives even come with the software. If not, Windows has a built in backup mechanism which is quite effective (especially the one that's in Windows 7!).
3rdly, if a lightning strikes your house, or a fire breaks out, the backup won't do you much good if you leave the DVDs next to the computer or leave the external drive connected. One should strive to keep the backup as far away as possible from the computer, although not too far. If you store it across town, you might have a good excuse to forget to backup. Also, if it's that far, you might become too lazy to drive over and get a file if you need it. A good solution could be to have a reciprocal agreement with a neighbor - you hold their drive during the week, and they hold yours. If you have an detached garage or storage shed, this could be good too (although, take care to prevent the drive from freezing or getting too much humidity).
Lastly, a backup that's untested will often fail you at the worst possible moment. You might discover that it hasn't actually run for over a month, or that some files are unreadable. A good practice is to test the backup around once a month. If you have a calendar like Outlook, you can use it to remind yourself to check it now and then.
One more thing - many people feel that buying a large drive just to store backup on is wasteful. In a way, that's true, but if you want to save some money there, you might consider getting a refurbished drive. These are inherently less reliable, but since you can easily detect if it stops working, it could be a suitable solution anyway. Also, keep in mind that you can activate folder-compression on it, as performance is less of an issue, and so use a drive smaller than your main one.