An ancient capturing game.
Lasca, sometimes called Laskers, is a board game invented by the chess master Emanuel Lasker. It is played with draughts pieces on a chequered board.
Terrace is a board game with a multileveled board. It has won many major awards, including Mensa's Best Mind Game of 1992. (Though it probably gained more popularity from being used as a prop in Star Trek: The Next Generation.)
Checkers variant with a shrinking hexagonal board.