Rough definition: pretty much a nation-state that is centered around one city for most of its economic life. It also has to be defined in terms of being part of that city, not a common ethnic heritage like true nation-states.
I think the Venice is about a large as a city-state can grow. Maybe a little bigger. As it was, it was the dominant naval power in the Mediterranean for a while.
I don't think that city-states can last for long after the middle ages. After that, success in war becomes much more about manpower and wealth, neither of which are in large supply to city-states. Also, to get real wealth and power after the middle ages, you need colonies, and colonies require a much larger initial investment that city-states can afford. Thus, after the middle ages, it becomes much harder to maintain your independance on your own against much larger nation-states. You are pretty much forced into being the vassal of one or the other. You can only maintain some degree of independance by playing the major powers off against each other/ being neutral in pretty much every major war. After the rise of nationalism, it becomes pretty much impossible, with nationalism undermining your state frm within. There are only three city-states in existance today, and two of them were formed from deals between larger nation-states (Singapore, Vatican)