You can stuff insulation to muffle the sound a bit, but to soundproof anything, you do it the right way or don't do it at all and the right way can be a little costly.

I will agree you can stuff sound deadening insulation into the ceiling and then cover that with either drywall or a dropped ceiling it will help but it will muffle the sound not kill it.

Use sound-dampened drywall or layers of standard drywall and Green Glue. This will do little for flanking sounds, but will be enormously helpful. For impact sounds, consider carpet and heavy padding on the floors above. Stuffing insulation between the floor and ceiling provides a barely measurable STC reduction.