A classic two-player abstract strategy game that deserves more attention: Lines of Action!

About Lines of Action, from BoardGameGeek:

Lines of Action is a simple game that uses checkers board and pieces. Its rules were published in Sid Sackson's A Gamut of Games. There are some commercial versions available though. The object of LoA is to get all your pieces into a single connected group. A group of pieces is connected if they occupy an unbroken chain of adjacent spaces, horizontally, vertically, or diagonally.