The answer given by another commenter, that unless the room is able to reach an equilibrium concentration of ethanol, all ethanol will evaporate from the glass, without stopping at any specific point, is absolutely correct. (Specifically, at atmospheric pressure and 20 degrees celsius, this would be around 5.8% ethanol in the atmosphere--and I think you'd probably notice if the air you're breathing was 5.8% alcohol)
However, as someone who googled this exact question out of curiosity after downing a glass of vodka that had been left out for several days and is currently feeling rather tipsy, I can personally attest to the fact that this is not the complete story. You see, the equilibrium state (i.e. the state that this system will naturally tend to approach over time) is a state where all the ethanol has evaporated from your glass. However, this tells us absolutely nothing of the rate at which this will happen. You see, as the concentration of ethanol decreases, the rate of evaporation will decrease as well. I'll admit that I'm not knowledgeable enough about chemistry (my background is in chemical engineering) to provide any hard numbers about how the rate will decrease, but intuitively speaking it should be rather obvious that it would. After all, if the equilibrium state is for there to be no ethanol in the cup, then surely the farther you are from this state, the greater the thermodynamic driving force will be. Also the rate could be slowed by a number of other factors (as the other commenter mentions), such as the shape of the glass or the pattern of air currents in your room.
Now, as the other commenter mentions, in order to provide any hard numbers about how much ethanol is left in your cup, we would need to know a lot more information (most crucially the time you left it for), but I'd be willing to bet that as long as there's still a significant amount of liquid in the cup there will still be enough alcohol to at least get you tipsy. Just don't expect it to still be at 40%.