"Does running the air conditioner in your car use more gas? I was always told that this was true."
It does. The compressor that drives the air conditioner puts load on the engine, and that makes it consume more gas than doing without it. As others addressed, using the A/C can be more or less efficient than other methods of cooling the car like driving with the windows down, but it'll certainly use more gas than doing nothing. In older cars, you'll also notice a hit to the horsepower, but newer cars generally use the computer to compensate so you won't notice it as much unless you're driving in mountainous terrain with the A/C running full out.
"What about running the heater?"
This will take less energy than the A/C because it just requires the blower running, since heat just gets taken off the engine. In most cars the hit to fuel efficiency will be small enough not to be noticeable.
"Yes, running the A/C uses considerably more gas than running the heater. My mpg went way down to 25 and lower over the summer, and back up to 27-28 in the winter."
That's not all on the A/C unit. In summertime your engine will need to run active cooling a lot more than in the winter, and that eats gas whether you're running the A/C or not. Active cooling (fan running) versus passive cooling (just the air passing through the radiator and engine compartment) is one of the reasons why stop-and-go driving consumes so much more gas.