In early cities, you could choose to make farms out of cities that have more than about 65% corruption under rep with FP. As the game progresses, you can decrease that depending on the present improvements to 50% or so. If you are far in the game, and the new city does not have the needed improvements for being productive, you could make them farms even at 50% corruption rather than spending 40 turns building whats needed.
Growing a city beyond size 6 often requires an aquaduct. At some point it will require a marketplace for happiness, and it would require culture to expand its borders if you want more than 8 tiles for your citizens to work.
Extra cities on the other hand provide you with more unit upkeep and with 1 shield production and one commerce even if it's completely corrupt. Therefore, it is better to have many small towns than 1 big one.
So you get about 20 productive cities in your core, and the rest of the world can be filled with small farm towns. 200 of them is not uncommon.
They are always usefull, in the beginning however they are mostly busy producing more settlers and workers (at 1 shield per turn since they are corrupt). These settlers and workers are needed to make more farms and irrigate all the ground around them. Cashrushing some settlers helps to get things going. This causes a kind of ever increasing avalange of settlers and workers. When you got this properly going and you are producing more settlers and workers than your army can capture ground for, you start shifting them to specialist farms.
Start to prepare your new lands for this as soon as you conquer them, this may even be in ancient age. In civ, you should mostly be trying to increase your number of citizens as much as you can, as soon as you can, so that as what you are doing with all the settlers, workers and irrigation while you conquer the lands. Without railroads, they towns are worthy, but as soon as you have railroads, they truly start to shine. When you get 200 of these farms, each providing 3 scientists, you have 2000 beakers per turn there already, enough to do any industrial age techs in 1 turn. They are so efficient that i prioritize on millitary to capture land for farming over building libraries until halfway trough the middle ages in a research game.