It's interesting to hear some people report that playing on a projector is tiring. I'm the opposite, I find the big screen to be the most comfortable. I think just about any game is improved with a projector. Even Wii games like New Super Mario, or strategy games like Civilization V are much better on the big screen. But here's some games I think particularly benefit from a projector: Assassin's Creed series, Uncharted series, and Shadow of the Colossus (especially in 3D).
Recently I've been playing Minecraft. For convenience sake, I usually play it on my laptop screen or on my 32" LCD. When I can though, I hook it up to my projector. Without a doubt, that's the way to play it. The big screen really brings out the landscape and vistas and immerses me in the game.
No input lag to speak of. I have a Mitsubishi HC3800 and an Acer H5360BD.