This past week I played a game with my 3's that's similar to Ring Around the Rosie. I select a child to sit in the middle of the rug. The rest of the children and I hold hands and walk around the child singing:
Will you be my Valentine, Valentine, Valentine
Will you be my Valentine, my friend _____!! Yaaaaay!
The "yay" is when we all fall down and then clap.
The child that was in the center then picks one of their classmates. We continue until everyone has had a turn. Simple, but they love it! I didn't think it was anything special but they request we do it.
You can modify this by having the child in the center dance around in their place. My 3's are still working on making a good circle so it's easier to have the child be sitting, but they can still wiggle while sitting though. You could also do different movements such as tip-toe walks and marching.