Commercially they're used as neutron generators for when you need longer lifetimes than ion-beam neutron generators: http://www.nsd-fusion.com/

A modified version (accelerating electrons instead of fuel ions, using magnetically shielded and actively cooled superconducting accelerator grids) shows some promise for actual power production: http://en.wikipedia.org/wiki/Polywell

Yes: Winning science fairs.

On a more serious note, I suppose one of these devices could be used as part of an apparatus for doing a novel experiment.

It's an excellent platform for learning about high voltage components, deep vacuums, particle physics, and monitoring and control systems.

I would hazard a guess that learning might be a practical benefit. Otherwise, as sbierwagen pointed out, no, not really.

I'm not saying that the effort was wasted. I just wanted to understand if this type of reactor had any direct practical benefits.