This video (from Hush Soundproofing in New York) talks about how they soundproof a ceiling. The original video I inserted in this post in 2009 no longer exists, so I've edited this post to include this clear and helpful explanation from 2021.
Their process involves multiple materials and processes for addressing noise. They remove the drywall that's already on the ceiling and spray any gaps they find inside the open cavity to seal them (pipes, etc.). Then they insert two layers of sheetrock between the joists, against the subfloor upstairs, combining it with mass-loaded vinyl (MLV).
Like most soundproofing experts these days, they use Roxul Safe 'N Sound insulation and they also use Rockwool Comfort Board. Then they attach a resilient channel to the joists (to keep the new drywall from touching the joists), and attach a layer of drywall to the resilient channel with more MLV.
I would have used QuietRock drywall instead of regular drywall, because it's already dampened, but I think their use of MLV in multiple layers might make this unnecessary. They must be getting good results, because they've got happy customers in New York, which is a very noisy city!
(edited this post in 2023)