Here in California it's illegal to wear headphones while cycling:
27400. A person operating a motor vehicle or bicycle may not wear a headset covering, or earplugs in, both ears. This prohibition does not apply to any of the following:
(a) A person operating authorized emergency vehicles, as defined in Section 165.
(b) A person engaged in the operation of either special construction equipment or equipment for use in the maintenance of any highway.
(c) A person engaged in the operation of refuse collection equipment who is wearing a safety headset or safety earplugs.
(d) A person wearing personal hearing protectors in the form of earplugs or molds that are specifically designed to attenuate injurious noise levels. The plugs or molds shall be designed in a manner so as to not inhibit the wearer's ability to hear a siren or horn from an emergency vehicle or a horn from another motor vehicle.
(e) A person using a prosthetic device that aids the hard of hearing.
Amended Sec. 45, Ch. 594, Stats. 2003. Effective January 1, 2004.
So, the law does specifically point out bicyclists as well, at least here in CA (and generally, bicycles are considered vehicles anyway under California Law, with some exceptions). One ear is okay, speakers are fine...
As far as practically, I usually don't use them at all, but sometimes I'll pop one in my right ear. In my experience, you use your ears far more than you realize. It's not something you really concentrate on, it's simply another source of information to have at your disposal. I'm sure there are probably studies out there (not related to cycling) that basically shows this.
That said, the point made that people drive cars without being able to hear much is certainly valid. You certainly can drive with loud music... but if I'm operating a vehicle that I'm far more likely to die in in the event of an accident, I'm going to make as few tradeoffs for safety as is practical. That's just my view, though. Different strokes...
EDIT: I guess some people have been cited...
http://www.cbs8.com/Global/story.asp?S=9513516
EDIT EDIT: I originally posted this in the necro thread linked here... deleted it. My bad.