So... I'm sure there's plenty of other methods, but this is what I usually do to block the annoying music from playing! A complete step by step tutorial with accompanying screen shots.
1. Use Firefox as your browser
2. Download and install Adblock Plus (added benefit of blocking other crappy flash advertisments and stuff) from http://adblockplus.org/en/installation
3. When you visit someone's profile now, scroll down to the bottom where you see the music applet. When you move your mouse over it, a tab that says "Block" will appear as below, click on this.
4. Select the 1st option (the one that ends with .mp3) to block that some from ever playing again.
Now when you visit that persons profile, you won't have to hear his/her music anymore.