Budget Insulation Advice

I live in an apartment with relatively thin walls. The only way to avoid neighborly complaints is to play music at a level where my receiver isn't as detailed as I want to hear. Basically I want to know if there's any cheap (read not specifically designed for this purpose) way of insulating the wall. The wall is probably around 125 sq ft and I really don't want to spend more than $200 for the project. Looks aren't important and I don't need to sound-proof just reduce the amount of sound that passes through the wall. Also would you have any recommendations for compensating for the newly 'deadened' room.
You probably won't ever make the neighbors happy.I have my own home and the neighbors hear my music 30 yards away in their homes.I just turn it down a bit when I know they are getting ready for beddy by.I listen to the bass heavy rock during the day and early eve then spin the mellow stuff later t night.You have to be careful no one calls the cops because then you will always worry even more.It hasn't happened to me YET! Try some large pieces of carpet padding on the wall.Maybe 4x6 then find some nice looking tapestry or rugs to cover the padding.Or get head phones to use at night or other times the neighbors are home.
more ideas: try weather stripping around windows,doors etc.Caulk cracks around the baseboards.stick a towel against the bottom of the door.All this may help a bit.Or you could just say screw it,get real drunk,blast the music until the cops come and tell them you are an audiphile and you can't help it.I'm sure they will understand........
If I had a dime for every time I wanted to do exactly that, (turn it up and wait till they came a'knocking) I'd buy my own house and pay off the cops to let me play as loud as I wanted... Unfortunately, however, I live across the street from the 6th precinct in NYC--so the cops actually ARE the neighbors I have to worry about pissing off. All considerations of hardware aside, the single most important upgrade on my wishlist is a better place to turn the whole mess on. I feel your pain.
You might look at "Sound Studio Construction on a Budget", F. Alton Everest, for ideas. Maybe your local library has it or can get it for you on loan. It's a great book for other aspects of room treatment too, so buying it wouldn't be a waste, even if it offers no workable solution to your problem.