Spend a little time getting ready to cope with a problem before you have one. All recent Macs come with a bootable CD-ROM with System software—keep it handy. If you own a copy of Norton Disk Doctor or DiskWarrior, keep it up to date and be sure that it will boot your CPU. It's also helpful in many recovery situations to have an external storage device like a FireWire hard drive. It's even better if you install a bootable system on that drive.
My hard drive has trouble getting going, but it always starts after a few tries. Should I bother backing it up?
No, your data is of no importance and you can probably recreate it within a few months. After all, you have lots of paper printouts to recopy from and you're a fast typist.
Seriously, if your computer or hard drive is doing anything unusual—squeaking, chirping, having trouble getting going, read/write errors, missing or damaged files—take it as a reminder to do a complete backup to another drive, removable media, or over the Web. Please!
How do I know what version of the System software I have?
Click on your desktop. Then click in the Apple menu at the top-left corner of your screen. The first item will say "About this Mac" or "About this Macintosh" or "About this Computer." Inside there will be the version of your System: 7.1 or 8.5.1 or 9.2 or 10.2.1 or something like that. This window also tells you how much (built-in) memory you have.
How do I know what Mac I'm using? [9 & X]
If the Mac is vintage 1997 ...