For businesses it is obvious that the vast amount of data (at the time of writing this, tens and hundreds of gigabytes, if not terabytes) make high capacity tapes the medium of choice for backup.
Large data centers cannot live without tape libraries AND offsite tape storage and rotation, to cover against the case of a disaster.
Believe it or not, tape drives are also the best backup for a home system as well.
Of course, some people will jump in right now and object to tape drives with various arguments. These arguments are mostly flawed as per the discussion below. Most of them come from people who only have experience around PCs or PC operating systems (e.g. Windows), and no exposure to how mainframes/mini-computers used to be, nor how data centers are run.
Let us address them one by one:
|Who needs backup when you have RAID
||RAID is local to one machine. If that machine catches fire, or gets stolen, the data is no where to be found. Moreover, RAID does not protect you from user error. If you delete file or a directory by mistake, RAID will not help you one bit. Only a backup on a separate media / directory will help with these "Oops!" mishaps.
|Tape is old and obsolete technology!
||Tapes are definitely old as a concept. But the technology keeps evolving, with more capacity and speed all the time. There are also robotic tape libraries that handle the insertion / removal of tapes from drives, although these are beyond home use.
|Optical media such as CD-Rs and DVDs are better!
||Optical media now are either CD-Rs (approx 700 MB each?) or DVDs (4 GB each?). These capacities are not enough to backup an entire disk today. Moreover, the media is mostly write once, so it is throwaway, unless you use CD-RW, which are too small, or DVD RW, which is still nascent technology with high cost drives and media, as well as low capacity compared to tape.
|IDE disks are so cheap. Just buy another disk, and put in the computer and use it only for backup.
||While that helps a bit, it is still flawed. If the original hard disk fails, this will protect you. However, if the power supply blows up and fries all components and drives, you are out of luck. You are also out of luck if you get your basement flooded or have a fire.
|Firewire external drives or IDE hard drives in a caddy are better and have more capacity
||These are certainly a step above the RAID argument or the optical media one. They will help you with the scenario where the server power supply catches fire. They will not help with other scenarios though. If you keep the disk at home, then a fire at home destroys your data AND the backup of that data. Moreover, you only have one copy of the data, so if you delete a file by mistake, then do a backup, that backup does not have the file on it.
|rsync mirroring does the job for me
||It depends on how you set it up. If you set it up to a remote machine (offsite, at work, university or at a friends place), then it is much better than the above options. However, do you keep multiple versions of the backup for a month or more? If so, then congratulations, and you are lucky to have all that space and resources! If not, then you have the same drawbacks as above. A local rsync over the LAN is relatively fast, but again, it is in the same home, subject to theft, flooding or fire.
You can read more on how I use tapes on Linux to backup a home network, where are there are lots of details on the hardware, configuration, and commands used, as well as lots of links to various information on backup.