1366x768. It's a widescreen laptop display. But I'd happily display anything 1024x768 or lower, as some games I've downloaded do that.
1366x768 is the maximum my computer will display. So I make everything 1024x768. Cheap monitors don't display too high, so I imagine a cheap-skate might not be able to reach the higher resolutions some people have.
Add that some people has net-books now, which display lower resolutions, that I am not sure how high they go. Though I can't imagine a net-book being used for gaming.
So I too would argue your best bet is '1024x768'.
Oh and I have a Dual Core Processor - look at me, Mr Fancy-computer pants.

(Sorry, I had to make a mockery of your request)