It is a well known fact that you like your headphones mostly because they let you hear your music and only your music. If, let's say, you take a walk in the park, or work hard in the office, or, for instance do some house-work, like vacuum cleaning - then you won't be able to hear a thing from outside. Or would you?
The fact is, it very much depends on the headphone type. If you want minor noise reduction, you can choose passive noise reduction headphones or even circumaural headphones that cup your ears and minimize the amount of sounds that travel in and out.
But if highly efficient noise-proof is what you want, then you should go for active noise cancelling headphones.
You might as well keep in mind that covering ambient sounds by raising the volume is not like playing safe. You could even damage your hearing irreversibly.
These devices have one tiny microphone on each ear-side that reflects the ambient sounds back-way, before they get to your ears. Most noise cancelling headphones use batteries to power their noise-cancelling circuits.
About the style of wear: around-the-ear and in-ear styles are more fit for noise cancelling use.
Examples
Editors from C|Net rate three noise cancelling headphones models, from different manufacturers as "very good".
Sennheiser PXC250
This is a pair of comfortable over-ear headphone system, that includes a noise-cancelling circuitry. The Sennheisers are available for $150.
All noise cancelling models can be used with the noise cancelling function on or off. When the circuitry is activated, and in silent environments, usually you can hear a mild hiss. This becomes inaudible in noisy places. However, some users complain on that aspect.
Sony MDR-NC11
These are some small but highly capable earbuds. The noise cancelling circuitry works great and the overall sound is excellent, a quality you would usually expect from heavy circumaural sets. You can have them for $149 a pair.
Bose QuietComfort 2
The Bose noise cancelling headphones made it to number one. They cancel ambient noise efficiently, they include a carrying case and you can have them for a 30-day home trial period. They're listed at $299; that's not really a bargain price.
Other noise cancelling headsets available:
Koss QZ-2000
,
Sony MDR-NC6
,
Panasonic RP-HC100
.