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It is commonly recognized that eliminating weight from a vehicle will aid it's acceleration. Even greater gains in acceleration, or wheel horsepower, can be made by eliminating weight from rotating parts of the drivetrain and chassis. To even further complicate matters, there are more gains to be made in reducing certain areas of rotating mass than others.
For example: Reducing 10 lbs of weight from parts that rotate at engine speed (crankshaft, flywheel, etc.) will have more benefits than reducing 10 lbs of weight from parts that rotate at axle speed (hub, rotor, wheel/tire, etc.) This somewhat relates to drivetrain loss, which most people are familiar with.
However, even reducing the weight of parts that rotate at axle speed, still far outweighs the benefits of reducing weight from non-rotating parts.
My 2002 Kia Rio in stock form was rated at 96 HP at the crank, but dynoed at a mere 76 HP at the wheels. Though there are other factors involved in getting power to the ground, such as spring rates and aerodynamics, rotational mass is a major factor in the significant difference between crank horsepower and wheel horsepower.
Another real world example of rotational mass that I was not pleased to learn was that my new tires and wheels were 4 lbs heavier on each corner and I actually dynoed lower HP and torque numbers at the wheels. So, if you have bigger wheels than your factory set, you will most likely make your car more powerful by swapping in your old tires/wheels.
The only problem with smaller tires/wheels on a performance oriented car is there may be a sacrifice in handling. Indeed, my stock tires/wheels were completely inadequate at harnessing even the moderate power gains done to my Rio. So, although I am suffering some power loss due to increased rotational mass of my drive wheels/tires, the gains in handling are an acceptable compromise.
There are other benefits to reducing unsprung rotational mass (the part of the car not supported by the springs: tires/wheels). Reducing unsprung mass, specifically from rotating parts, will not only improve acceleration, but it can greatly improve handling and braking too.
Some examples of common aftermarket parts that are manufactured to be lighter than OEM parts to reduce the effects of rotational mass are: bearings, flywheels, drive shafts, crankshafts, rotors, hubs, tires, wheels, ring gears, differentials, clutches, transmission gears, and possibly the most common application, pulleys.
Sources: www.cyclecat.com
Chassis Engineering by Herb Adams
www.tirerack.com