One Finger, One Thumb
Source: "Songs to Sing Again & Again"

One finger, one thumb, keep moving

One finger, one thumb, keep moving

One finger, one thumb, keep moving

And we'll all be happy and gay!

(Alternate last line: "And we'll all be merry and bright!")

Actions: for each verse, stick out or point to the body part(s) currently being mentioned. Repeat the song until you have added on one hand, two hands, one arm, both arms, one foot, two feet, one leg, both legs, stand-up-sit-down!

Thanks very much to Michael Clark, who emailed me this alternate ending to the song:

One finger, one thumb, one arm, one leg, a knock on the head, stand up,sit down, stick out your tongue, keep moving...