Hosted servers, cloud computing, and backups
For all that we roll our eyes when people have only online backups or redundancy and suffer data loss as a result of it, I don't think it's necessarily as easy to do things the 'right' way as we make it sound, or even feasible at all in some situations.
Suppose that you are a modern, efficient Internet-based business, and so you are running your servers the smart way; instead of building your own machine room in a corner of your office space and bringing in expensive network connections, you've just got servers in someone's hosting center. Further suppose that you have a non-trivial amount of data.
So, how are you supposed to get offline backups? To do them, you need either frequent physical access to your hosting center in order to keep going in to swap disks (or tapes), or you need high bandwidth to your office in order to copy the data over to an office machine that you have convenient physical access to. Both of these options can be expensive, sometimes substantially so, which may mean that online backups are your only feasible choice.
(You can't really automate offline backups; if the backup media can be brought back online by remote control, it is not really 'offline'.)
And if you have enough data, backups probably become completely infeasible. For example, I doubt that the various cloud storage operators like Google (for Google Mail et al), Amazon S3, and so on even have online backups of the data in the cloud, much less offline ones; I suspect that they are dealing with so much data that all they have is redundant copies spread across datacenters.
(The advantage of live redundant copies is that they are immediately and directly useful, which makes them more affordable than pure backups.)