Most people sitting for long periods of time tend to slouch or bend forward. Taking the back of the chair off won't help in that type of situation. Sometimes having a lumbar support across the low back can put the spine in a position of slight extension. This position may help reduce low back stiffness.
The chair you sit in is important, but so is your workstation. Even more importantly take frequent breaks and move around. Even if all you do is stand up and stretch and then sit back down again, this can help reduce fatigue and prevent injuries.
A popular new desk chair without a back is the use of a Swiss ball designed for this purpose. Some people use it without a stand, but a supportive base is available and keeps the ball from moving out from under you.
We hope to see some studies in the near future to show whether or not such a chair design is beneficial.