As the question says, the answer is a microphone. Ignacio is correct that "most microphones" which today means electret mics, do not generate electricity, but "dynamic" microphones (with coils moving in magnetic fields) do.
You may be able to generate nanowatts up to microwatts this way.
But that's the end of the good news...
Power = energy/second
1 Watt - 1 joule/second...
Energy (mechanical) = force * distance
1 joule = 1 newton * 1 metre
Force = pressure * area
1 Newton = 1 Pa * 1 m^2
And pressure ...
1Pa = 94dBa.
What I don't have offhand is the amplitude of a 94dBa signal (displacement of air molecules and hopefully diaphragm in millimetres) but it varies with frequency. Now by observation of a big speaker cone, you only get displacement measured in mm at low frequencies : let's plug in a peak of 1mm at 100Hz for now, for a velocity of 2 * 1mm * 100 per second or 0.2m/s. This gives us an upper limit for the displacement of an air molecule 1m out (where SPL is usually measured); it's probably considerably lower than this...(We can plug in different displacement/frequency if we find better figures; they won't change the conclusions by much)
So a 1m^2 array of microphones in a 94dB sound field could theoretically produce ... 1Pa * 1m^2 * 0.2m per second or 0.2W.
Note that one big microphone would experience cancellation across this area (sound would be pushing one part of the microphone while pulling another) so be much less efficient.
So that's not very much power for a substantial size (and cost) of generator.
Note that a solar cell of the same size can produce about 150W or 750 times as much power, and it'll be cheaper to boot.
If you have such a loud sound source - let's say a big diesel engine - look at energy recovery directly from its exhaust, there may be four orders of magnitude more free energy there.
So it's not impossible, but it's usually not an attractive prospect...