This is something that I like doing in any game that can readily be beaten in a few hours;
I do not allow myself to ever get a single Game Over, and if I get one, then that's it, and I have to restart the whole game.
I think that this actually makes many games a lot more fun - not only does it make them more challenging, but it also makes you value every extra life a lot more.
I usually try playing this way in platformers, and right now I consider attempting Mega Man 1 for the NES.