Backup solutions are not the same as high availability solutions. They have different purposes and picking the wrong one for the wrong reasons may be disasterous.
A backup solution is a one that creates separate copies of data that can be used to restore the original in the case of data loss. A high availability solution is one designed to keep a system usable and available in the face of hardware (or similar) failures
Solutions like RAID, database mirroring, clustering and SAN replication are forms of high availability. They are not backup solutions and cannot replace good database backups. Having the database on a RAID array will not help if the DB becomes corrupt. SAN replication or database mirroring is of no use if a user somehow deletes critical records.
On the other hand, a backup strategy, however good, is not going to help much when a critical piece of hardware burns out and the business will be losing millions if the app’s not up within 10 minutes. If the app is critical, both backups and an appropriate high availability solution have to be considered. Picking the right high availability solution is complex. Entire books have been written on it.
The only time having no backups at all is an acceptable option is if it’s a system where the data can be completely recreated from another source with no difficulties (example here would be a reporting database that’s replicated directly from a different server)
Here’s another take on backups – http://www.sqlskills.com/BLOGS/PAUL/post/Importance-of-having-the-right-backups.aspx