Sid Meier's Colonization/Number of colonies

The problem with Civilization is that the only viable strategy in it is "smallpox", that is a lot of small cities located very close to each other (with 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 the highest difficulty level, the limit is a mere 5 royalists before you get a -1 penalty to everything. That kinda explains the current situation in the U.K. ;-) This is very serious because you get the -1 even if the rebels are a majority. To get a 20-population colony without a -1 on Viceroy you need the support of at least 75% of the population (well, a few % less due to rounding). If you have 70% support there, the colony gets -1! (-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 liberty bells.
 * 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. A big enough fleet of ships to stand in for wagon trains would be even more expensive
 * Fewer problems with the Indians.
 * Less micromanagement. Having 30 colonies functioning efficiently is a lot more work than 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 a 1-citizen city vs. 200 for a 19-citizen city)
 * As far as security is concerned, distance between your outermost colonies is much more important than the number of them. Because the competing strategies are "Few big colonies, far apart" and "Many small colonies, close to each other", the difference in the size of your empire is relatively insignificant. Inland colonies won't be attacked by the king, and usually most of your colonies are one round on horseback (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 a 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/cash crop 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, indentured servants and the wrong specialists, and is poorly located) than building a better one from scratch. Still, it weakens your enemies a lot, so you may want to conquer them just to harm your opponents.