How do I keep staff “busy” without creating meaningless “busywork?”

As an IT Supervisor, one of my biggest challenges is finding meaningful tasks for staff to do while waiting for calls during a Help Desk shift, or between project tasks. I hate even the thought of “makework” just for the sake of looking busy; that seems meaningless to me, and I believe it can lead to negativity. But I also think it’s unhealthy for the workplace to have staff sitting around browsing non work-related Internet sites, or just twiddling their thumbs during work hours.

This could be a simple matter of ineptitude on my part, but I’m betting I’m not the only one who struggles with this. Anyone have some good suggestions for meaningful activities?