I just played a game in which I had like 20 cities -- at least 18 I know, because I saw I had 18 theaters at the end of the game screens. I kept every city except two that had no culture so were automatically destroyed.
It made my research slow here and there, that's for sure. I was doing a very aggressive conquest style approach, and all but four cities were actually made by two of my enemies, who I wiped. When I hit the medieval ages I was sweating because my expenses were so high that I had to keep research down for a good long time.
However, once those cities started going, they really contributed nicely. That took a while, that's for sure. I thought someone was going to get a space race victory on me because they were a high ranked civ and were completing multiple SS Thrusters long before I was anywhere near that stage of research. Once I got that research done, though, I was able to stick pretty much every city on spaceship parts, and got them all done almost simultaneously. Big cities on the bigger pieces, little cities on the little ones.
And this was despite being quite a noob and making many mistakes and having setbacks. Frankly, my understanding of the game is not really very good. Yet it worked. I won and wound up higher than every civilization in every stat but one, and that was who had most soldiers. Funny since I spent most of the game fighting!
I find keeping cities is very handy because it gives your units first of all a place to get an accelerated rest in some security. This forward point in your enemy's territory also lets you see some of the possible paths he might be trying to run past you on for a retalation. And when the battle continues to the next city, this city comes under a little less pressure as it drifts farther behind your lines. Eventually this enemy city that became your city and forward base becomes part of your supply of new soldiers, which is very important. If you are waging a long hard war, you will lose a lot of units and need to send in replacements quickly, or lose your advantage as the enemy builds up an ever greater defense-specialized force. So when you try to keep that momentum going but your troops have to come from 20 tiles away, and all your wounded have to heal in enemy space, you lose a lot.
I'm sure it varies game by game how thin you can afford to stretch yourself. But if you're fighting only one AI at a time, you can stretch yourself pretty thin if you're fighting and pillaging the enemy down to a much worse place than you are. And if you start catching up even a little on the growth of the cities you capture, even if they're crummy ones, you get a phenomenal late game boom. Doing all those spaceship components in one turn was pretty cool. I'm still amazed I beat that AI that was so far ahead of me in the space race, and every thing else research wise, for almost the whole game.
One reason