Ramses

Each of the two players is trying to maneuver his four pieces onto specially marked squares or to box his adversary in (if he cannot move any piece, he's lost). On your turn you move first one of your own pieces, then one of your adversary's.

The pieces move orthogonally (as long as they don't go twice through the same square during a move) by as many squares as there are pieces in its starting column and row (using the larger number, counting itself).
The game has Chess-like qualities since there is no randomness at all, and each player has perfect information.