While it hasn't been updated in 18 months, the series of articles on Digital Outback Photo still contain a lot of good information about this topic. Just remember that software and hardware for backup and archiving have changed since the series was written.
A distinction should be made between backups and archival storage.
Conventionally backups are made to enable restoring to a previous point in time after something happens, e.g., a disk drive dies or a software glitch corrupts a directory. We (should) make or update backups pretty frequently, often writing over the oldest of several copies, as Chris mentions.
Archives, on the other hand, typically get added to, not overwritten, and we intend our archive to survive for a long time. The lifetime of the media on which we write our archive becomes very important, as does how and where we store the archive. Another important property of an archive is how readily the archived data can be located and read, something Chris talked about when he discusses organizing and naming photo files.
Just to get an archive started most folks should use two or more external drives, routinely adding new files to them and storing at least one copy somewhere away from the other copies.
Personally I keep one copy of pretty much everything on my main computer, a second copy on a second computer in the house, and a third copy on an online backup service. I rename files using Breeze Broswer (other tools will automate this, too) with the date and image number. I name the directory containing the files with the date and the subject and/or location. I format the date YYYYMMDD so sorting by name sorts in oldest to newest order. This approach means I don't have duplicate names, which simplifies sharing the files, as well as making finding a particular photo pretty easy.
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