Kiddo has always moved her hands, but within the last few days we have successfully taught her to "wave bye-bye" (obeys single commands- yes!). When Dad walks out the door for school, or when we leave the house, or when we leave a set of people, we tell her to "wave bye-bye" and she (usually) does her approximation thereof.
Sometimes she makes a fist and bends her wrist once or twice. Sometimes she moves her hand up and down.
My favorite application of this skill is while reading. The book "Oh my oh my oh dinosaurs" by Sandra Boynton ends with the page "Dinosaurs looking right at you to say good-bye because we're through." With no prompting from us she figured out that this was "saying bye-bye" and she waves to the dinosaurs. I love it.