Well I do have a projector and I have tried gaming on it. But it is too big for me, can't follow everything what happens on screen. 50" plasma- also too big, 26" LCD-even that is too big. For me 19-22" works the best.
However I use projector in clone mode when I have friends over while gaming on monitor but the rest can watch it on projector screen .
I have a projector which I've used for gaming. It works ok but it's a little too big and the picture is not as nice as my 22" monitor or even 46" TV.
One piece of advice I would give you is to probably avoid a home theater projector and opt for a multimedia projector if you're looking mostly for PC gaming (or even console gaming). There are several factors to consider with a projector, but home theater projectors tend to be designed for low light, movie type settings and not necessarily for games. They tend to have lower brightness and higher contrast which is great for watching video but not so great computer graphics.
Maybe you need to get used to the large screen size when gaming on a projector. But it's cool though, feels like being in the game itself. I do agree that brightness should be high because you mostly wouldn't darken your room for playing games. You would just like to switch on the projector and start gaming.
So basically, a multimedia projector would be a good fit as purplerat said, also educational projectors could do the job (education projectors need to have very high brightness as classrooms often are difficult to darken and sun shines through the windows).
Good projectors in this category are BenQ MP624 (3000 lumens), BenQ MP771 (3000 lumens, short-throw), Toshiba X150U (2600 lumens) or NEC NP400 (3000 lumens).
I also use a projector. I've tried PC games on it but I'm not much of a fan. Xbox 360 games on the other hand are great. Usually when I play it is with at least one other person. With 4 people, everyone gets a 32 inch at my place!