Longer answer: Implementing a SAN first increases the choices of backup systems immensely (LAN-free backup, server-less backup, etc.). However, your current situation can not be evaluated from afar.
From my experience it is often possible to take away the pressure from backup by categorizing the data stored and thus minimizing the data that needs to be backed up. Instead of backing up all data, only data that is worth it and has changed should be backed up anyway.
Certainly IT cannot decide what the value of certain data, i.e. whether or not it is worth being backed up. This is a valuation that only the owner/user of the data can make. However, I have found that IT can support that valuation process by the user tremendously by implementing a charge-back policy that puts the cost for storage back to those that use it.
That way, you might be able to take away the biggest pressure from backup and can start with planning and deploying a SAN, without running the risk of over-purchasing hardware and backup software.
Hope that helps.
Read Jamie Gruener's response to this question.
This was first published in June 2004