The most common problem I encounter is crashed hard drives. This WILL happen to you at one point or another in your computing life. Hard drives are mechanical, and mechanical things can fail. Also, you may think you are being backed up, but have you checked recently? The second most common problem is backup system failure. Check your backup system periodically to ensure it is actually working. Some cheap and easy options:

Mac Users:
If you have the new System 10.5 (Leopard), just buy ANY external hard drive and plug it in. The built-in backup system will ask if you wish to use it as your backup disk. Click "yes." That's it. Your Mac will get backed up several times a day.
Information on Suitable External Hard Drives

If you have an older system (10.4 and below), buy a Western Digital "MyBook." Plug it in and double-click on the "Software" folder. Follow the directions.

Information on Western Digital MyBook

PC Users:
The Maxtor OneTouch external hard drive is the simplest solution. Just plug it in and follow the easy, on-screen instructions.
Information on Maxtor OneTouch

Note: none of theses hard drives should cost more than $120.