Also, if the wiring, ducts, and pipes are recessed above the bottom edge of the floor joists, you can nail furring strips to the sides of the joists and then attach your ceiling material to these strips. This would leve the edge of the joist exposed for the "exposed beam" look.
Even better, you can build three sided box beams that slide over the edge of the joists and then nail them in place so that all of the beams are level. This will allow you to put drop ceiling panels on top of these box beams. The beauty of this approach (if you have the space) is that you can remove the drop ceiling for running wires and repairs, while at the same time preserving your headroom.