I'd like to sound proof my basement as I live in a bungalow and the music is quite loud in the bedrooms above.

I'd like to listen all night and not disturb people upstairs. How can I do this?
To really soundproof a room is difficult and expensive. Most people get by with dampening the sound using insulation between the floor above and the basements ceiling. This can be pretty effective, but you will still have sound/vibration transmitted through the floor joists and the up-stairs walls.

Have you tried a good set of headphones?
We recently wrote an article on sound proofing. It's on our resource page. In the column titled "Rives Articles". It should answer some, perhaps all, of your questions.
I'd like to do this economically. My plan is to build a room within a room. I want to fill the ceiling joists with acoustic insulation available at Home Depot and then drywall over top (2 ply if needed.)

Then I will put in a drop ceiling leaving a gap between. For the side walls I plan to use the same type of insulation then drywall overtop then leave a gap and put in another drywall all the way around with staggered studs.

I realize this won't be perfect but do you think I can get about a 50% reduction in noise upstairs? If so then I'm happy.

Should this plan be changed somehow in order to obtain my 50% noise reduction goal?
Recommend using Roxul fireproof batts between ceiling joints and wall studs.
Kel--A room within a room is the ultimate in sound isolation. When building it's not that much more expensive--but you eliminate structure born vibration. The only way to step it up is to consider the floor (putting a sound absorbing matt under the subfloor), the HVAC--this can be a major sound leakage and is discussed in the paper. Doing a room within a room will not be effective if you have major sound leaks like the HVAC or recessed cans (we see that mistake often).