If everything stored on your computer has absolutely no value and you don’t mind setting everything up again you can forgot about backup.
For everyone else you MUST do this REGULARLY or possibly one day, without warning (or at least it’s likely you won’t see it coming) your data (pictures, business accounts, music, CV, Will etc) will be gone. If you are using a conventional hard drive it will probably still be retrievable but it may involve specialist facilities and probably cost more than your computer! However if the drive is mildly misbehaving I can quite likely recover most of the data.
If you suspect your computer or hard drive is failing, this generally is NOT the time to attempt a backup as you may just accelerate the problem and possibly, depending on how you are performing your backup, overwrite a perfectly good backup with a bad one.
The single most important rule is you should have at least two copies of all important data.
Your data can be saved amongst other options to:
Another hard disk (easy to use, good size but still mechanical)
Optical disks (Little harder to use, very good for off-site, you can just use more disks as you need more space)
Memory stick (cheap if you don't need many, easy to use but small storage space)
Online (some broadband providers provide some free space as do some photo printing sites - often referred to as the cloud)
Paper! (make sure you check the permanence of the ink particularly inkjets)
It’s not exciting but it doesn’t have to be difficult. Peace of mind can be achieved very simply.