FM Transmitter Circuit
Probably the audio signal going into the base of Q1 isn't strong enough.  Microphones vary widely in the strength of the signal they put out.  This circuit is clearly meant for a electret microphone, which generally produce larger signals than most other common types.  If you have a dynamic or condenser (unlikely) mic, then the signal will be a lot weaker.  Make sure you really have a electret mic.

If it still doesn't work well with the proper mic, try adding a little amplification.  From the general looks of this circuit, I'd say that the microphone signal shouldn't be more than 100 mVpp, probably significantly less.  You can experiment by using the audio output of a radio or preamp or whatever other source you have lying around.  Put a resistor divider on the output to attenuate it.  Start with 50 mVpp and see how that works, then adjust the level from there by listening to the FM radio and also checking how far the signal spills into adjacent bands.