The 3-2-1 Rule

The simplest way to remember how to back up your images safely is to use the 3-2-1 rule.

    We recommend keeping 3 copies of any important file (a primary and two backups)
    We recommend having the files on 2 different media types (such as hard drive and optical media), to protect against different types of hazards.*
    1 copy should be stored offsite (or at least offline).

*While 3-2-1 storage is the ideal arrangement, it's not always possible. A second media type, for instance, is impractical for many people in the ingestion or working file stage. In these cases, many people make do with hard-drive-only copies of their data. Best practices, however, still require 3 copies and some physical separation between the copies.

Threats

In order to design a backup system that works for you, it's important to understand the kinds of problems that can lead to data loss. Let's take a look at some of the dangers that threaten your data's well being and examine some solutions.
Device failure

Any digital storage device can fail. Hard drives fail all the time, and even a multi-drive device can fall off a table and be destroyed. In order to provide real backup, a backup copy of the data needs to be on a separate device, such as an external drive or different media like optical disc.
Viruses

Viruses can propagate silently from one storage device to another, and then strike to destroy data. All rewritable data is potentially vulnerable to viruses (even on Macintosh), so any hard drive data is at risk. Write-once storage, like Optical disc provides the best protection against virus.
Malicious damage

Your archive can be exposed to other malicious damage, either from anonymous hackers or perhaps from people targeting you personally. Any computer that is online is theoretically vulnerable to hackers, although an enterprise-level firewall can offer lots of protection. The best protection is offline, and preferably offsite, storage of backups, as well as write-once media storage.
Volume and Directory glitches

The Volume and Directory information on your storage media are a map of where the files are stored, as well as a table of contents. If these get corrupted, then the computer may not be able to find the files on a drive. Aside from basic maintenance of your file system, the best protection is the use of write-once media.
Transfer corruption

Any time data is transferred from one device to another, there is some possibility of corruption. This can be because of problems with the RAM, drive, connectors, bridgeboard, network, or cables. The best protection against transfer corruption is to transfer files with a utility that performs a validated transfer. Use of write-once media can also help to prevent transfer corruption (after the initial creation of the disc).
Read more about validated transfers
Lightning strike/Voltage surge

Excess voltage from a lightning strike or a blown power company transformer can fry your computer in a heartbeat. A surge protector might protect your computer from damage caused by this excess voltage, but provides no real guarantee of protection. The best protection is provided by the use of off-site, or at least off-line backups.
Theft

While video and photo professionals have always been exposed to theft, that hazard rarely extended to our footage itself. Since our pictures are now stored on expensive devices, they are now at risk. Protection against theft includes security measures such as an alarms or a safe, but is best accomplished with offsite storage.
Fire or water damage

Like film archives, digital images can be destroyed by fire or water damage. But unlike a film archive, it's possible to make a complete offsite duplicate of your digital archive for very little money, and thus to be fully protected.
Human error

One of the most common causes of data loss is simple human error. You can accidentally throw away or unintentionally modify files in some undesirable way (such as downsampling). Protection here is a little more complex, particularly for working files, since they generally can't be protected with write-once backups.

Off-line backups that don't get updated immediately are a valuable part of protection against human error.