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Your data is valuable. It will cost you time and effort re-create it, and that costs money or at least personal grief and tears; sometimes it can't even be re-created, e.g., if it is the results of some experiments. Since it is an investment, you should protect it and take steps to avoid losing it.
There are basically four reasons why you might lose data: hardware failures, software bugs, human action, or natural disasters. Although modern hardware tends to be quite reliable, it can still break seemingly spontaneously. The most critical piece of hardware for storing data is the hard disk, which relies on tiny magnetic fields remaining intact in a world filled with electromagnetic noise. Modern software doesn't even tend to be reliable; a rock solid program is an exception, not a rule. Humans are quite unreliable, they will either make a mistake, or they will be malicious and destroy data on purpose. Nature might not be evil, but it can wreak havoc even when being good. All in all, it is a small miracle that anything works at all.
Backups are a way to protect the investment in data. By having several copies of the data, it does not matter as much if one is destroyed (the cost is only that of the restoration of the lost data from the backup).
It is important to do backups properly. Like everything else that is related to the physical world, backups will fail sooner or later. Part of doing backups well is to make sure they work; you don't want to notice that your backups didn't work. Adding insult to injury, you might have a bad crash just as you're making the backup; if you have only one backup medium, it might destroyed as well, leaving you with the smoking ashes of hard work. Or you might notice, when trying to restore, that you forgot to back up something important, like the user database on a 15000 user site. Best of all, all your backups might be working perfectly, but the last known tape drive reading the kind of tapes you used was the one that now has a bucketful of water in it.
When it comes to backups, paranoia is in the job description.