The easy answer would be to simply nail or screw 2x lumber to the sides of the existing joists, with 1" hanging below the bottom of the joists.
Steve brings up a good point about access. A good idea was mentioned here a long time ago by a woman who framed as mentioned above, and wanted a nice looking, semi-removable ceiling. What she did was cut 4x8 drywall in half (to 4x4), prime and paint the surface, and attach to the framing with drywall screws around the perimeter only. Then, without tape or joint compound, she cut and painted (or stained) 1x4 pieces and attached to the ceiling in a grid pattern over the drywall joints. I believe she used decorative screws so she would not have to paint over them, allowing for easier removal. She could then take down (or replace if damaged) individual 4x4 sections for access to wiring, plumbing, etc. I am seriously considering this idea, as it is relatively easy and inexpensive, while perhaps looking a little nicer than traditional suspended ceilings. Also, while I can generally perform small repairs on drywall, I am not sure I would want to try to tackle all the taping and mudding on a ceiling.
I am also considering the above framing, and installing long, wide, rustic looking barn boards. No tongue & groove, and easy to put up/take down with screws. Not sure about fire hazard with recessed lighting, though.
Good luck, and let us know if you come up with any alternatives.
PS: My local paneling store carries a suspended ceiling product that has deep solid oak grid pieces that provides a recessed panel effect. Expensive, but much nicer looking than the traditional ones.