How long before someone posts an equation involving blackbody radiation in this thread?
edit: From an electrical point of view, P = V^2/R_sys where P is power, V is voltage, and R is the system's resistance.
If we ignore all this blackbody radiation mumbo jumbo to determine the brightness vs power, we can get an idea of what's going on.
The easiest (and most commonly used) method to create a dimmer is to put a potentiometer (the dimmer) in series with the light such that R_sys = R_bulb + R_dim. The voltage supplied is constant at 120Vrms.
So the power used by the system is V^2/(R_sys+R_dim). Clearly any value of R_dim will reduce the power consumption. Also, by voltage division, we know that the voltage povided to the bulb will be V*R_bulb/(R_bulb + R_dim). However, as others have said, the relation between brightness and voltage is not linear so it's difficult to tell exactly how much power you save by dimming the light.