The original post is VERY long... so for this time around, I'm breaking it into a number of separate posts - which I will link to from one post when they're all published.
As a general note, this guide attempts to stay away from sweeping generalizations of what strategy or tactic is "best". There is seldom a best strategy or tactic (such as "always build a city if x happens, or a settlement if y happens"). Instead, I try to represent each concept as a series of choices to be made, and the advantages and disadvantages of each. Settlers has too many factors (many beyond your control) to come up with some sort of formula to win in every situation. Instead, you need to be flexible and adapt as the game progresses. Don't be afraid to try out new strategies, as you may need them someday.
This guide assumes you have only the Kosmos (German version) or Mayfair (US version) Basic set. Many discussions also refer to elements of the 5-6 Player Expansion set, and the Kosmos Seefahrers / Mayfair Seafarers expansion set (referred to as "Seefahrers" in this guide). These two expansions, while adding some new game elements and rules, do not substantially change the overall game mechanics. Later editions will address the Stadt and Ritter Expansion in a separate section, as it in essence creates a new game.
Your choice of strategies will influence your initial setup and overall game play. The separation of strategies below is a bit artificial, but useful to understand the concepts behind them. In practice, players will use a combination of these strategies.
The Ore-Grain Strategy
This seems to be the most popular strategy, at least in the basic game. This strategy attempts to get a lot of ore and grain early in the game, in order to produce cities as quickly as possible. You should focus more on ore than grain, as you will need three ores to build a city, versus two grains (and in the basic game, there is usually less ore available then grain, as there are only three ore hexes compared to four grain hexes).
This strategy is often so powerful because the first cities you produce will probably be on your initial settlements, which should have high production values. Other people going for settlements right off will probably be left with lower production-value intersections. (Chuck Messenger
In general, the more congested the board, the harder this strategy becomes. Other players (especially wood-brick players, as described below) will have a greater expansion potential as they can pump out roads and settlements faster, thereby blocking off your expansion. All too often a player at the endgame will find themselves with the maximum of four cities and zero settlements for eight victory points, and not being able to get another two settlements (and corresponding victory points) because they are boxed in. In the basic game this is not as much as a dilemma as you can get another two points with the largest army or by victory point cards; in games where you need more victory points this can be more problematic. When playing with (or against) this strategy, you must keep in mind its greatest weakness is this lack of expansion potential.
The Ore-Grain Strategy can be good for Seefahrers, as it is harder to get boxed in (simply build to an island). Getting an ore or grain port is great for this strategy, as after you build four cities you won't have as much a need for these resources, and it can make the endgame a lot easier.
Remember that by building cities, you are concentrating production in fewer locations. As you are putting more of your eggs in fewer baskets, make sure you don't leave any vulnerable. As pointed out by someone else later in this guide, make sure that you don't place your cities at an intersection with one good number and two bad numbers, or the robber can make your very expensive city worthless. This will be much less of a problem to players who are concentrating on (many) settlements rather than on (fewer) cities. For this same reason, those variants that use multiple robbers/pirates can hurt people who concentrate on cities more.
Near the end of the game you will be the constant target of the robber, as ore and grain become valuable to the other players. You need to have been saving knights so that you can get the robber off your production units. Also, since you have cities, your production spaces will naturally look like better places for the others to put the robber. (Trevor Hyde)
The Wood-Brick Strategy
This is a strategy to get a lot of wood and brick early in the game, in order to build settlements and roads fast.
A wood/brick port is very useful in this strategy, as finding a way to get ore/grain will be important to build cities for the middle to end game.
Lots of people think this strategy is less effective on a small or congested board, as you need room to grow. Actually, it can be more effective, as your increased road building capability gives you the advantage in reaching those limited number of expansion spots first. An ore-grain player's worst nightmare is playing on a congested board with one or two wood-brick players.
This strategy naturally lends itself to getting the longest road.
For this strategy, it is very important that you build new settlements around open grain and ore hexes, or you will have a very difficult time trying to build cities later on in the game (which can be crucial for a win).Optionally, with your increased settlement production, you can build on a number of ports to get ore and wheat. (Mike Schneider
The Card Builder Strategy
This strategy is similar to the Ore/Grain Strategy, as it involves getting Ore/Grain hexes and building two cities fast. Then, cranking out development cards. This player will get an inordinate number of Knight cards, allowing them to keep the robber off their hexes and get other resources by stealing from other players. Often, victory point cards will come up. At some point in the game, try for a third settlement or city. The largest army is practically guaranteed. (Chuck Messenger
The Balance Strategy
This strategy strives for a balance in all five resources. Settlements can be built relatively quickly, and the player is less likely to be boxed in. Also, this strategy leads people to become more self-sufficient, and less likely to require trading. (Chuck Messenger
The Rare Resource Strategy
A friend let me know I was missing this one
Basically, this strategy is about identifying the rarest resources, and making sure you have access to them. There are two types of rare: rare in overall production (due to bad numbers being on them), and rare in position availability (fewer number of hexes have the resource, like ore and brick in the basic game, which only has three hexes each instead of four hexes like wool, grain, and wood). In many cases both will happen, such as when ore and brick have bad numbers on them in the basic game.
This strategy is not a monopoly: you don't necessarily want to be the only person on these hexes (as seen in the Monopoly strategy below, this may not be such a good idea). You just want to make sure you have them. This could be taken to the extreme, for example a player who goes for ore and brick, because they are the two rarest, but is more commonly used along with another strategy. This strategy can work well with a Cartel strategy, described below.
The crux of this strategy is realizing that you will pay dearly for rare resources later on in the game, and so you should plan ahead by getting them early. A reduced overall production value early in the game to get those rare resources is usually more than offset by not making 3:1 or 4:1 trades later in the game to get them.
The Common Resource Strategy
Every game usually has a very common resource, that no one in particular wants. This is usually wool, as it is often the odd man out. The Wood-Brick players and Ore-Grain players (the two most popular strategies) will only be trying for wool if it is convenient. A friend of mine
The Monopoly and Cartel Strategies
These are strategies to gain either exclusive control (monopoly) or shared control (cartel) of a particular resource, usually ore or brick as they have the fewest number of hexes in the basic game (three, versus four of all the others).
First, the Monopoly variant, to gain more or less exclusive control. It is usually attempted by trying to control all of the good hexes (usually just one) of a resource by yourself. It seldom works. The major problem with this strategy is that the robber almost always sits on the monopolized hex. As you are the only person on that particular hex, the robber will stay there until YOU get it off (or a seven is rolled), unlike shared hexes. Also unlike shared hexes, every player EXCEPT YOU considers that hex to be fair robber placement territory, especially since they want a chance to grab that monopolized resource from your hand.
A potentially better way to try the monopoly strategy is to let other players surround the best hex of that resource, and to go for the two less marginal ones (in the case of ore and brick). Then try to place the robber on the good hex throughout the game. This has the advantage of being able to place your initial settlements away from the rest of the crowd. You will need a lot of lot of knights, to get the robber off of you, and onto the best hex. (Mike Schneider
The Cartel variant. Basically, this is a strategy to share control of a particular resource in order to reduce the problem of the robber in a monopoly, but to make sure that you are the dominant player in that cartel. In this variant it is only necessary to control most of the resource. For example, if you control two out of the three settlement locations on a good hex of a rare resource. The other player will work just as hard to keep the robber away, but will only collect half as much. This is most common on a good ore hex. Another way this can be done is by having majority access to several hexes for a commodity for which you have a port. The other players can't keep the robber on all of them, and will probably just keep it on your prime hex. Sheep and wheat are most typical of this kind of cartel, because they are not the commodities that people usually target during initial placement. (Mike Schneider
The Straight Numerical Advantage Strategy
This strategy really tries to maximize production, without concentrating on any particular resource. Just get as much of anything. You may need to trade a lot, because you could end up with a strange mix. This works better in games with more people (more people to trade with). A 3:1 port is probably essential, if you have a varied mix of resources.
I put this in because some people use it, but this is not really a strategy. A good strategy is a plan to let you get the particular combination of resources you need to get certain victory points, which this does not do. This could be good in the initial setup as a short-term plan, before you figure out what other strategy you will need to win.