Jesper Juul, an academic studying games and a self-styled "ludologist," is putting together a history of matching tile games, starting with Tetris and Chain Shot and spanning down and outward. Though he calls them the "most disrespected and despised game genre there is," he's worked out a very neat and eloquent classification system, and I bet there are many of us here who could add titles to Juul's list. He asks, "Am I missing a game that contributed to the history of matching tile games? Do you find the connections playsible?" Check out his diagram and see what you think.
It's some nice research, but I'm not sure I agree with the formatting of the chart from a clarity standpoint. This is a very good basic idea though and one I'd like to explore and see explored in similar ways for other genres and game types.
I have approached this in a different way in my unfinished article. In that I am classifying puzzle games in 2 broad categories (though I deal briefly with other game types too). I have "pit-based" games (Tetris, Puyo, Panel De Pon, Dr. Mario) and also what I call "arena-based" games (Boulderdash, Lemmings, Solomon's Key).
I further subclass pit based games into symbol matching(Puyo,Baku Baku) and shape-building(Tetris, Quarth).
I attempt to draw up a feature list for each broad type of game (and illustrate each with some example games) and then attempt to arrive at combinations of features that may derive a new game...
I have still to complete this but this has given me the impetus to get my finger out!