Well, something in your circuit is not working correctly, because I have the same circuit assembled on a breadboard right now and it's working properly.
I'm using 1n4148 diodes, and my "100k" trimpot only measures 82k, but the circuit also works fine with a 50 k pot. Also tried it with a 100 nF timing cap instead of 10 nF and it works fine with either pot using that capacitor as well. Duty cycle is smoothly adjustable from under one percent to over 99 percent (measured at Pin 3). I'm driving a IRF3205 mosfet with a 47R gate resistor, with an incandescent lamp load, and also tested it with a computer fan (but the fan drops out at duty cycles less than about 18 percent, not surprisingly).
I even tried it with plain old 1n4004 rectifiers and it still works full range, although not quite as well at very short (under 5 percent) duty cycles.
I would also suspect a burned pot in your circuit.
ETA: what version of the 555 are you using? I'm using NE555P.