A lot of how quickly polish dries depends on application technique (keep your coats thin and your results will be better!) and texture (glitter polish, for example, almost always dries more rapidly). But there are also a few formulas everyone in our office agrees are particularly fast and effective. The drugstore standby is, of course, Sally Hansen Insta-Dri, which really does set in a couple minutes, applies super easily, and comes in an impressive color range. Our resident polish expert Elizabeth swears by Nars nail polish; she says even though it's not specifically designed for quick application, it still hardens up in no time and, just as importantly, lasts a long time without chipping.
You can also always just use whatever polish you want and then put a drying agent on top, of course. Essie Drying Drops are great as long as the polish underneath isn't too thick. Which it shouldn't be, because... again, light coats!