In my home I built the Theater room into the core plans. I used 9 inch thick foam form walls for the below grade exterior walls. I also extended these walls around the perimeter of the theater room. After the forms are in place (like lego blocks), they are trimmed at the top for level (easy) and then filled with concrete that creates a "mesh" of concrete and foam.
Above the foam wall (the blocking) is SilentTruss system that replaces conventional 2X10 floor joists. But the name Silent is only in regards to walking on the floor above from squeeks. As a material it is very thin and passes noise quite readily from room to room. So, the answer was to use spray foam on all blocking on exterior walls (great cold insulator) and to use it on interior walls for noise blockage.
Now, for the ceiling. In my theater room, I put 8 inches of fiberglass roll insulation between the ceiling joists (floor joists for the room above). Below that I have a track ceiling system where I have handmade coffered ceiling tiles inserted. The ceiling is probably the weak sound insulation component in my system. If I were to do it again, I probably would have put some heavy (really heavy) vinyl material stapled to the bottom of the ceiling joists that is made for this purpose as another sound insulation layer. This still would allow access to plumbing / electrical above if needed to be peeled down (unlike drywall).
In the rest of the lower floors, the ceiling is drywall. The drywall is mounted to "Z" strips where the screws holding up the drywall goes into one side of the metal Z strip, and the other side is then screwed to the ceiling joists. This allows the drywall to be sound insulated from the joists minimizing sound transition. You can also use these Z strips of walls. They take up about 1/4 inch of space. For partition walls, you can also stagger space 2x4 studs every other so that the inside drywall and the other side drywall are mounted on different studs for sound insulation. Effective wall thickness is then typically same as 2x6 wall. I did this for walls that had to hide large steel posts that support the roof structure and had to be 2x6 anyway.
All interiour walls (which because my house is post and beam construction and therefore has few interiour walls) are filled with fiberglass insulation for sound. All floors / ceilings have fiberglass as well.
Doors: In my theater room, I used an exteriour grade door that included a full frame and gasket system. The door (steel) was also filled with pourable foam to further insulate it. Makes for a very solid door with minimal sound leakage.
Exteriour walls are 2x6 and cellulose filled. Excellent for both it's insulation and sound deading properties. I have several walls that are 2x4 that are inbetween window banks. These are insulated with spray foam for its higher R value and the structural stiffening that it provides.
Obviosly insulation for exteriour walls makes economic sense as well as sound insulating reasons. On the interiour, it makes for a more pleasant living space.