How many kings is it possible to have on the board at once?
For American checkers on an 8x8 board, it is possible to get 24 kings on the board from the initial position. Here is a Java applet with a proof game of 211 moves.

For International draughts on a 10x10 board, it is possible to get 40 kings on the board from the initial position. Here is a Java applet with a proof game of 389 moves.