Sid Meier's Colonization/Number of colonies

The problem with Civilization is that the only viable strategy in it is the "smallpox", that is a lot of small cities located very close to each other (strongly overlapping ranges).

In Colonization you will typically build 10-20 colonies, slightly fewer on lower difficulties and slightly more on higher, because the Tory corruption -1 bonus is a very benign problem at Conqueror, but a huge obstacle for colony development on Viceroy.

Good things about having many colonies:
 * Big colonies can quickly become corrupt. On highest difficulty level, the limit is mere 5 royalists before you get -1 penalty to everything. That kinda explains current situation in the U.K. ;-) This is very serious because you get -1 bonus even if the rebels are a majority. To get a 20-population colony without -1 bonus on Viceroy you need support of at least 75% population (well, a few % less due to rounding). If you have 70% support there, the colony gets -1 bonus ! (-1 not 0, as +1 bonus for >=50% support is not given if there are too many Tories). It almost doesn't matter on easy levels, but is the main smallpoxing factor on Viceroy.
 * There's a limit of 3 people working in a single building. You're going to need many cities just for the tools, arms and other required factories. Especially for producing bells of liberty.
 * Each colony has 1-2 special squares (3 or more do happen, but rarely, 0-specials is usually a bad site for a colony). More colonies means more special squares.

Good things about having few colonies:
 * It costs less to build all necessary buildings with fewer cities. Every colony should get a Newspaper, a Warehouse, and later some protection.
 * You need a lot of roads and wagon trains to transfer the goods between colonies. The sufficiently big fleet of ships would be even more expensive
 * Less problems with Indians.
 * Less micromanagement. Having 30 colonies functioning efficiently is a lot more work than with only 5.

What doesn't matter much:
 * The free production from the central square is much less crucial than in Civilization. Unlike Civilization growth rates are not inversely proportional to city size (20 food for 1-citizen city vs. 200 for 19-citizen city)
 * As far as security is concerned, distance between your outermost colonies is much more important than number of them. Because the competing strategies are "Few big colonies, far apart" and "Many small colonies, close to each other", the difference in size of your empire is relatively insignificant. Inland colonies won't be attacked by the king, and usually most of your colonies are in a one round of horsewalk (if you build roads between them) from one another, so you can quickly transport armies where they are needed.
 * Every colony produces horses if it has a food surplus, but their value isn't that high.
 * Every colony gets a bit of free stuff from Indians, but it's usually not worth much.

I usually set up a few inland colonies for getting lumber/ore/(maybe cash crop). They *should* have food deficit, they're more efficient when they're small, additional farmers would only lower efficiency, and the wagon trains are going back and forth anyway to get their products to the ports (but you may put some Farmers there later, when the support is high enough). Bigger, typically coastal, colonies produce food, have factories and a system of education. It's reasonable to have one or two inland food/cashcrop producing colonies if the places you find are really great.

Terraform. Conifer/Mixed Forests are very useful for lumber, but most other forests without specials would be more valuable cleared and plowed.

Conquest can get you some free colonies, but the computer player mismanages them so much, that you may actually spend more time fixing the colony (which contains mostly criminals, servants and wrong specialists, and is located in a horrible place) than building a better one from scratch. Still, it weakens your enemies a lot, so you may want to conquer just to harm others.