I'm about to try some sound treatment in my NYC apartment. It's a small 10 X 10 room. The walls joining my apartment with the neighbors is very thin and sound is easily transferable from my apartment to the neighbor's. I want to get the best bang for the buck. I plan on stripping the 2 walls that connect to the neighbor's of their drywall so as to reinforce the wall with more studs. (I'm concerned about the weight of any soundproofing materials that I hang) I am then faced with what to put inside the walls before reapplying the sheet rock. I'd thought about using Auralex's "sheetblok" or "DB block" (which are the same thing) on the inside of the wall and underneath the carpet and padding. What other products should I use inside the walls? Any other suggestions would be greatly appreciated.

This is a acoustic forum not a sound proofing forum... But I think you are going to do a lot of work and not have that good of results. The only way you are going to stop sound from getting to the next room is to build a room with in a room. I am sure the land lord will love you for that!!
You could try packing the walls with fiberglass and double dry wall, then put a 2" spacer then dry wall again. But even with all of that your neighbors will be knocking to tell you to TURN IT DOWN!!!

The Sheetblok stuff is not the best "bang for the buck". look here for the best advise. http://www.usg.com/Design_Solutions/2_3_2_flank_sound.asp

First off I'd have to ask whether you can do all that construction to an apartment. Out here in Ca you can't do anything, even mount a shelving unit or something.
Given that disclaimer and you can proceed you'd have to describe what you intend to do inside your room, music wise..how loud you're going to be. Then describe the wall construction once you dismantle the drywall on your side. If it's a regular 2x4 interior stud wall you'd be coming awfully close to poking through or doing some damage to the neighbor's wall. You wouldn't want to build a double wall as detailed above as this may lessen the bass isolation as opposed to building something correctly. More mass is the key to isolation.

I helped a friend with his Condo. We filled the wall cavity with rigid insulation then drywalled 5/8" with half schedule screws then a layer of Celotex then another layer of 1/2" drywall held back from all sides with 1/4" spacers pulled out and caulked after screws. this gave him enough isolation to practice playing along with a boom box fairly loudly.

Thanks a lot for the input. Sorry I wasn't more specific. To clarify, I own the space, and can do what I want. I'm about to have some renovations done and I'm enlisting this company to do the work to my studio room as well. They know nothing about soundproofing so it's a case of the blind leading the blind. I need to figure out a way to treat these walls as best as possible while being able to direct others to do the actual work. I realize that this won't be actually "soundproofed" and I'm not looking to play a drum set or loud guitar amps. I just want to be able to play music at a reasonable level, strum an acoustic guitar and shout in to a microphone. Even this, I realize is no small order. The room is very bright and has an extremely live sound to it. This seems to add to the transfer of sound through the walls.

witesol, could you tell me what rigid insulation, celotex and half scheduled screws are? Also, what are these "spacers" you speak of?

Thanks again for the input guys. I sure do need it.

OK, cool. much easier if you own the joint! ..and if you're not doing drums.
you're basically in the construction phase of the walls and such, the soundproofing part. Once you're done isolating yourself to the level you need then you go about treating the inside of the room for better acoustics with some traps, foam or curtains...
as far as the constuction specifics I'd ask here and go poke around the johnlsayers.com site for a couple days then come back here and get some acoustic advice, there you can find out about 703 insulation, Celotex(pressed soundboard you can buy at Home Depot) and installing the drywall screws(half schedule just means half as many).