I am finishing up work on my game Enyo, a 2 player, single system, competitive arcade/abstract puzzle game.
There is a tutorial, a quick battle mode, and a tournament mode where you can specify a variety of different parameters, such as how many rounds to play, whether to play to a score target or a time limit, etc. Basically I'm trying to make a fun little game you can play with a friend, room-mate, girlfriend or boyfriend or whatever.
In this game, both players control the same object, a red ball in the center of the screen. One player can only move the ball up and down, the other player can only move the ball left and right. There are black and white balls flying across the screen, and one player is trying to get the white balls, the other player is trying to get the black balls. It sounds pretty confusing, but everyone that has played it so far has gotten it in just a few seconds and the feedback I've received has been really positive, everyone seems to enjoy it.