How to eliminate noise from PWM controlled 12V fan at low speed
I had the same problem with a 5V fan.  Something simple worked for me: To decrease the PWM frequency.  You probably want to do this using pin 9 or 10 (for the Uno) as changing the frequencies of other PWM pins messes up the delay and millis functions.  Details on how to do it and a very convenient function are provided in http://playground.arduino.cc/Code/PwmFrequency.  In my case, using the lowest frequency possible (31250/1024 = 31Hz), I completely eliminated the hum for higher speeds and significantly reduced it for lower speeds.  And by the way, I used the PWM pin to drive a MOSFET since the current of my fan was 140 mA, much higher than the 20 mA Arduino pins can safely provide.