Set in the world of Homeric myth, The Odyssey is a level-based casual game in which you have to guide your ships from one end of the level to the other in the face of monsters, storms, and other obstacles. What's interesting (and innovative) about it, however, is the control scheme--you move your ships by holding down the mouse button and drawing in the water to create currents, and by changing the direction and strength of the winds by moving the mouse within a wind-control region of the screen.
In other words, the physical actions you take to play the game are quite different from the norm. The results can be frustrating at times, because you're affecting your ships indirectly rather than directly, and getting the result you want is sometimes a challenge--but that's part of what makes the game interesting, of course.
The Odyssey was winner of the Popcap Casual Game Award at the Slamdance festival in 2006, and also named one of the top ten indie games of 2006 by Game Tunnel.