Good question. To find out, I checked with the leading manufacturer of dimmers in the world, Lutron Electronics. Lutron's founder, Joel Spira, invented the dimmer back in 1961.
Lutron does not recommend using their dimmers with CFLs, including those CFLs that are marketed as dimmable, because the quality of the dimming does not meet Lutron's standards. Though there are no safety concerns, a CFL will flicker noticeably when dimmed, and will not dim to as low of a level as an incandescent bulb, but shut off instead.
However, you might want to consider that dimmers used on incandescent bulbs do save energy. An incandescent bulb dimmed by 10 percent consumes 10 percent less energy than a bulb on full light and the bulb will last twice as long. Similarly, a bulb dimmed by 25 percent uses 20 percent less energy, and the bulb will last four times longer. Finally, a bulb dimmed by 50 percent uses 40 percent less electricity, and the bulb will last 20 times longer.
Dimmers are a great option for saving energy in rooms where homeowners also wants to be able to create scenes and moods for different activities. For the perfect energy saving combination for your lighting needs, I'd recommend a combination of both CFLs and dimmers on incandescent bulbs.