Some bikes, I think children's bikes or a certain type do. Usually the pedals will just spin backwards and make a neat sound, it won't actually pedal in reverse. Bikes usually have brake levers on the handle bars that control brake pads on the front and back tires; right lever for back tire, left for front, in my experience.

The only bikes I can think of that will actually go backwards from pedaling backwards are toddler bikes like a tricycle or toy bikes. That might be why the image has him sitting backwards, because generally it'd either stop the bike or just spin the pedals doing nothing.