That is a tough question to answer in the abstract. I think a good production city should be able to produce your top military unit in 1-2 turns. So, say, 20-30

in the classical age (for Axemen and Horse Archers) with the potential to produce at least 100-150

by the end of the game.
Science cities are harder. The problem isn't so much as how many

you need in any given city but how much total you can generate across your civ. You want to be researching at an average of about 5-6 turns per tech. This
thread gives a good analysis of the numbers involved in each era. (Note that he starts out with a rate of 10 turns/tech but later updates that to 5. Also note that he is talking about a Specialist Economy which you didn't ask about and he has since changed his mind about some of his conclusions. But the raw numbers are still useful.) So by the Classical era you want to be prouducing at least 60-70

across your empire. If you have 3-4 science cities, that comes out to 15-20

in each city. In the industrial age the average cost of techs is about 2400

so, if you have 5-6 science cities you will want about 75-100

per city. The modern age is about twice that (if your game lasts that long).
Note in addition to having several science cities, you should have one Super Science City that puts out about 2-3 times as many

as the normal ones. This is often the GP farm in my games, but I suppose it need not be. This city will get the great library, the academy (built by an early Great Scientist) and, eventually, Oxford University.
I have nothing particular to say about commerce cities. Generally "as much gold as possible" seems to be my rule of thumb. Obviously you want these guys to pay for a good chunk of your maintenance and have some left over for upgrading/rushing units and other nice things. I generally have one city dedicated to commerce in addition to the capital (which benefits from Bureaucracy) but I have never given much thought to how much is enough.
Edit: I just realized that futurehermit's analysis doesn't give raw numbers for Renaissance through Modern periods. I must have crunched those numbers myself. Here is the breakdown by era:
Classical: 315 average

/tech
Medieval: 733 average

/tech
Renaissance: 1528 average

/tech
Industrial: 2367 average

/tech
Modern: 4186 average

/tech
Note that these are averages and the high and low techs in each age can be quite deviant. So one may take 12 turns whereas another will take 2 or 3.