You know that active noise cancellation (ANC) headphones don't actually reduce the volume of people's voices, right? If anything, it makes them seem louder by canceling continuous sounds (aircraft engines, background rumbling, that sort of stuff) that would otherwise mask human voices, music, babies, etc. In the end, all you're doing is replacing the non-annoying noises with your music.
What you really want is a pair of in-the-ear phones (
like these) that act like earplugs. They're much better at making things quieter (nothing like your boss talkng behind you for a few sentences before he realizes that you aren't listening to him); they're smaller (pocket size) and more durable (no bulky parts to break); they don't require batteries, and they protect your hearing by allowing the use of lower volume levels.