Make regular backups.
Be certain that everything on your system is backed up.
Formulate a written backup plan. Remember to update your plan whenever you update your system or change its configuration.
Make paper copies of critical files for comparison or rebuilding your system (e.g., /etc/passwd, /etc/rc, and /etc/fstab).
Make at least every other backup onto a different tape to guard against media failure.
Do not reuse a backup tape too many times because the tapes will eventually fail.
Try to restore a few files from your backups on a regular basis.
Make periodic archive backups of your entire system and keep them forever.
Try to completely rebuild your system from a set of backups to be certain that your backup procedures are complete.
Keep your backups under lock and key.
Do not store your backups in the same room as your computer system: consider offsite backup storage.
Ensure that access to your backups during transport and storage is limited to authorized and trusted individuals.
If your budget and needs are appropriate, investigate doing backups across a network link to a "hot spare" site.
Encrypt your backups, but escrow the keys in case you lose them.
When using software that accesses files directly rather than through the raw devices, consider remounting the filesystems as read-only during backups to prevent changes to file access times.