This one-switch game by Jack le Hamster sees you in "the story of a paralyzed man who can only used his right hand." You fly his arm-chair from left to right, seeking to put some wrongs right in the world. Land in the right spot to give a person a lift then take them where they can do the most good.
Your control is the Space Bar to fly up and right-wards. Release to sink down and if over a level surface, land and stop. This does require a very high level of skill, but you can't die, and there's no time limit.
I am also impressed by the other two games also hosted at Dobuki.com being a manic one-switch chase game called OMGAF Dragon! and the point and click puzzle game World of Turtle which I think should be a great fit for eye-gaze play.
Via: Lundum Dare.