Apart from the obvious dangers of online attack, there is the ever present danger that your hardware may fail, or be stolen.
If you have years of family photos, important documents, and files you can't be without, you absolutely must back up your data in more than one way.
A single backup is better than no backup at all, but it's far safer to have multiple back ups.
Imagine you have a full backup to an external hard drive, but your house burns down or you're a victim of theft.
Both the original and the backup will be gone.
To protect against this, backup online or off site.
The caveat here, is to often check the integrity of your backups, to make sure that in the event of having to restore data, that data is what and where you expect it to be and viable.
Backup items you just cannot live without to a portable hard drive, and keep it kept locked away.
Backup the same items to an online storage facility like Jungle Disk, Mozy or Carbonite or Crashplan for Mac.
This gives your extra protection, because your backup is off site and in the Cloud.
Hard drives are cheap, keep an up to date clone drive of your main hard drive within your computer, by using an automated software backup routine.
If it all goes wrong, you can boot straight into your clone drive.
We also LOVE Dropbox for small file backups and file sync.