I publish that my rates include "some" furniture moving. In practice I will work around a couple smaller items per room (lamps, coffee tables, etc.), and maybe a couch and la-z-boy in their living room w/o charging extra. If I get to a house and there is furniture everywhere and they expect me to move it all I tell them the amount of furniture will significantly increase the time it takes so will have to charge extra. I had one person reschedule and the next. Most people try to get the areas pretty clear, or have been trained by previous cc'ers pretty well.
Charging by the sq. ft. solves this problem very nicely. They want the carpet cleaned under the sofa? Just put the sofa on the plastic furniture gliders I send out with my package, slide it out a few feet, vacuum, and clean it. It usually takes less than a minute to clean the usually already clean 20 or so sq. ft. of carpet under a sofa. At my own sq. ft. rate, that means another $8 on my invoice.
Try to train your customer to remove all what I call "clutter" type stuff before your arrival: toys, piles of old National geographic magazines - that kind of stuff. Makes your job go much faster. (Do this on the phone while setting up the appointment.)