I like board games where one player's move narrowly constrains the opponent's next move. Of course, most two-player strategy games involve such constraints of some sort, e.g. in the sense that after one player has moved her black piece in Chess, the opponent has to move his white piece. But I'm concerned here with games which employ stronger versions.
For instance, in Kamisado there are pieces of different outer and inner colors. And as an opponent you must move a piece with your constant outer color (black or white) and the inner color corresponding to the color of the field that the other player has last moved to. So you must move a particular one of your pieces by constraint.
For instance, in Quarto the two players are supposed to put four pieces in a line with a twist: if the four pieces match in either color (black and white), height (large or small), or shape (rectangular or round; with or without hole) match, there is a winner. And as an opponent you must make each own move with a piece that the other player selects for you. So again, you must move a particular one of your pieces by constraint.
Which other games of this type and what other types of constraints (more narrow than just color as cited for Chess above) do exist?