Maritime: Pros Amazingly Broken. You dont need food for cities anymore, make them in the middle of the desert and they will thrive as specialist cities. Capitals can make settlers every turn with all that food bonus and if your using Liberty.
Make nonstop settlers with your capital because it will produce them soo fast. Have the cities be founded the minimum distance away for optimum results, doesnt matter what the lay of the land is. Connect with road, make a colosseum and have city stop growing at size 4. Keep doing this and you'll never have problems with money, happyness and you'll be soo outproducing everything in the game that it make deity games rediculously easy.
Cons: When you lose the citystate, due to capture or out of influence cause you insta built a factory..., it slows you way down.
Culture: Pros Very awesome at adding culture, highly recomended to have one. If your mass expanding like you should it is necessary to have them otherwise it will be a very very long time to get Communism and be ubergodly.
Negatives: none really, you keep them till you don't need them then you conquer them and add another city.
Military: Pros: Free artillery pieces. In an epic game where it would have taken me 57turns to build one, they gave me one every 20.

bonus units are always good. Military city states actually fight wars with you, ive seen them invade their neighbors that we were at war with and provide ample distration.
Cons: getting a free unit and having it spawn 100 years away. Getting yet another scout on an island map.
I want another city-state type. One that adds Happyness per era. Call it Monaco, Andorra, Luxembourg, Liechtenstein. Basically tourist spots.