Why doesn't any air flow out of the vents in my 2001 Honda Civic?

It depends, you should always get air from the vents when the car is in motion if the re circulation button "is not" pressed. If you mean the fan isn't working you need to check for power at the blower motor.If there is no power it could be:1.The fuse for the blower motor is blown.

2. The blower resistor is faulty

3.The control module (knob assembly) is faulty or has a faulty wire in the circuit.

If you are getting power to the motor, the motor is seized/faulty.

Either the ducts are blocked , the blend doors are malfunctioning, the cab filter (if it has one) is plugged, or the blower motor isn't working.

Have you changed the cabin filter lately?