From my eleven-year-old daughter come these jump rope rhymes. She says they don't sing them, they are more of a chant than a song. They do this at school during recess.

Cinderella, dressed in yella, went upstairs to kiss a fella,
Made a mistake and kissed a snake, how many doctors would it take?
1, 2, 3, 4,...(count until jumper misses.)

Cinderella, dressed in blue, went outside to tie her shoe,
Goodness gracious, she'll be late. How many seconds did it take?
1, 2, 3, 4,...(count until jumper misses.)

Fudge, fudge, call the judge, (Sally's*) having a baby.
Wrap it up in toilet paper, send it down the elevator,
What shall it be?
Boy, girl, twins, triplets, boy, girl, twins, triplets...
(repeat until jumper misses)
*substitute jumper's name

Teddy bear, teddy bear, turn around,
Teddy bear, teddy bear, touch the ground,
Teddy bear, teddy bear, tie your shoe,
Teddy bear, teddy bear, I love you.

This last one I have also heard sung as a lullaby. The jump rope version has a different rhythm and may have slightly different words.

Another thing they do is call out the names of the 50 USA states in alphabetical order, one state per jump. When the jumper misses, it is said that she will live in that state.

Another chant consists of repeating H, E, L, P, until the jumper misses. Then the letter she misses on signifies what type of jumping she must do next - H for Hot Peppers or High Wire, P for Peppers, and I don't remember what E and L stand for. Nor do I know the meanings of the jump names.