Sound Proofing 101

Rives gives excellent advise.
Also if your speakers (or stands) are spiked into the floor, then try spiking them (via disks or coins) onto concrete paving slabs, laid on the carpet. This should provide a steady base while reducing coupling with the building structure.
IF this all fails I'd really consider getting a good headphone system. Senn600s plus an inexpensive amp ala Creek would allow you more freedom to enjoy the music.

If you are thinking of putting a covering on the wall, a company named Celotex makes some sound reducing material that is meant to be installed behind the drywall, but in your case, you could probably install it over the top of the drywall. We built a box out of the stuff and put a little boom box in there and it did a very good job at reducing the sound. You might want to look into it. It is fairly inexpensive.

I once was about to rent a house with one wall of my future sound room to be common wall with the neighbor. I did a fair amount of research on this problem.......

The best way to keep the sound inside your room is with a VERY HEAVY fake wall. There are several ways to do this. Far and away the cheapest way is to build a wall inside. (2X4's with sheetrock on each side.) Then fill the wall space you have created with sand and pray the sheetrock doesn't break open.
I didn't say it was easy, just cheap.

Richard
PS: I didn't rent the house.

This really requires two things. First, sound travels through everything in the room...not just the wall. It travels through the floor, the ceiling, any common airducts, etc.

Your best solution will probably be to make a wall, with a gap, as mentioned. The best way to do this (seeing you are using a full range audio system, would be to make a concrete cinder block wall using Helmholz resonators. You can get these from Proudfoot, they call them the Sound Blox. While not extremely cheap, they are very reasonable. If you cannot use these, use cinderblocks, and after the wall is completed, cut vertical slices through the outer wall of the cinderblocks every 24 inches or so. These act as a makeshift helmholz resonator. Then, apply drywall to the outside of this. Make sure to leave a gap of at least 6 inches between the existing wall and the new one.

If you want to go all out, then you need to float the floor as well. After your wall is complete, get some neoprene floor covering (expensive), and lay it atop of your existing floor, up to the new wall. Then put a layer of fiberboard subflooring and plywood flooring. Top with carpet, and you're set. In a residential area, there's not much you can do about the ceiling, but with the wall you should get an STC rating of about 40 (40 db down on the other side) and with the floor STC 50-55. Hope this helps!

Brian

First and easiest if the landlord approves is a layer of 5/8 inch sheetrock over the existing wall. Others have made suggestions for floor and air ducts and they are valid. Any air gaps such as around outlet boxes and switch boxes are problems. Don't forget the door and the door seals. The sound could be going out your door and in his.