If you're trying to detect the notes of a polyphonic recording (multiple notes at the same time) good luck. That's a very tricky problem. I don't know of any way to listen to, say, a recording of a string quartet and have an algorithm separate the four voices. (Wavelets maybe?) If it's just one note at a time, there are several pitch tracking algorithms out there, many of them mentioned in other comments.
The algorithm you want to use will depend on the type of music you are listening to. If you want it to pick up people singing there are a lot of good algorithms out there designed specifically for voice. (That's where most of the research is.) If you are trying to pick up specific instruments you'll have to be a bit more creative. Voice algorithms can be simple because the range of the human singing voice is generally limited to about 100-2000 Hz. (Speaking range is much more narrow). The fundamental frequencies on a piano, however, go from about 27 Hz. to 4200 Hz., so you're dealing with a wider range usually ignored by voice pitch detection algorithms.
The waveform of most instruments is going to be fairly complex, with lots of harmonics, so a simple approach like counting zeros or just taking the autocorrelation won't work. If you knew roughly what frequency range you were looking in you could low-pass filter and then zero count. I'd think you'd be better off though with a more complex algorithm such as the Harmonic Product Spectrum mentioned by another user, or YAAPT ("Yet Another Algorithm for Pitch Tracking"), or something similar.
One last problem: some instruments, the piano in particular, will have the problem of missing fundamentals and inharmonicity. Missing fundamentals can be dealt with by the pitch tracking algorithms...in fact they have to be since fundamentals are often cut out in electronic transmission...though you'll probably still get some octave errors. Inharmonicity however, will give you problems if somebody plays a note in the bottom octaves of the piano. Normal pitch tracking algorithms aren't designed to deal with inharmonicity because the human voice is not significantly inharmonic.
