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.