What can you hear through a "normal" wall?The average American home built after the 1940s probably uses gypsum board nailed onto wood studs over a hollow enclosure.
The STC rating for that setup is 30 decibels. According to this chart, normal conversation is still audible through a 30 STC wall. That should be no surprise to some of you apartment dwellers.
A single sheet of 5/8" drywall with fiberglass insulation provides an STC of about 40. You can still hear loud speech through this setup. If you use Roxul batts, you increase that STC rating to about 45.
If you use a soundproof drywall (like QuietRock) and insulation, you increase the coverage to 50 STC. Double drywall with Green Glue inbetween, plus Roxul insulation increases it to 56 STC. You can read about this at the Welk and Sons Drywall site.
The cost difference is noticeable: 5/8-inch "dampened" dry wall is about $80 per sheet compared to $10, but might prevent you from having to do more sound construction later.
These blog posts from Mason Chang tell his story of soundproofing an apartment and building a new wall. Let's hope it brought him lots of peace and quiet!