I noticed there were no articles in the strategy section for this game, so I thought it might be a good idea to write one. I have now played nine games of Hansa, most of them two-player games in the last few days, and I think I've developed a knack for playing it. When I first tried this game a couple of months ago, I thought it was dry and not terribly impressive. Now I think it is a very good game, with some important strategic issues involved.
First of all, how is there any strategy in Hansa when it is a self-proclaimed "tactical" game? Remember that strategy involves long range plans and the big picture, whereas tactics focuses on short range actions and the immediate situation. It is true that Hansa is a highly tactical game. The tax system eliminates the possibility of saving up talers or goods, and the board resources change periodically as well. One important piece of "strategy" is to realize the tactical nature of the game and play accordingly. On the other hand, there a couple of strategic elements that could easily lead to a loss if you neglect them.
In my experience, the essential strategy in Hansa is to set up all of your trade booths as quickly as possible very early in the game. This will cause you to sacrifice some juicy victory points, but it is well worth it in the long run. By saturating the board with your booths, you will dominate the market, which allows you to get free goods thereafter and also charge the other players talers. These are powerful advantages that outweigh the loss of converting goods into booths. You should spread your booths out so they cover as many cities as possible, particularly cities that hold more than one good and are frequently visited by the ship. It's important to keep your booths on the board by only selling goods when you have a lot of goods to sell. If you follow this strategy while your opponent neglects it, you will almost certainly win. If you and your opponent both follow this strategy, then it will be a tight game.
Unfortunately, this is a very transparent strategy. Unless your opponents are idiots, they will catch on to what you are doing after a game or two, and begin to adopt the strategy for themselves. Therefore, it might actually be more clever to avoid being obvious about what you are doing, and shoot for a majority of trade booths (more than your opponents) and not total domination. I guess this is a judgment call that depends on how observant you think the other players are. Once the cat is out of the bag and everyone is doing it, then get all of those booths out as quickly as you can.
A second, more subtle piece of strategic advice is to follow the Minimization Principle. This idea of restricting your opponents' choices applies in one way or another to most strategy games (e.g. Chess, GIPF games, Blokus). What you want to do is to minimize the other players' options by positioning the ship inconveniently after you take your turn. By inconvenient, I mean that you end your turn with the ship nearby empty cities, or cities that you control with your trade booths. You'll know this is working when your opponent says things like "Ack you've screwed me again" during the game. He or she will have to waste precious talers just getting the ship back into play, or give talers to you. This strategy may be most effective in a two-player game, but it's probably always worth considering, especially if you can do it at no cost. Don't just think about where the ship is going on your turn, think about where the ship will be going when your turn is over.
That's about it for strategy. Once these guidelines are followed, the game will be decided by the tactical choices of what goods can be bought and sold, and how the luck of the tiles plays out. Hansa is really fun to play when you begin thinking about these kinds of issues. Otherwise, it's just about taking turns moving the ship around the board. It took me a few plays to realize it, but in the end I raised my BGG rating of Hansa a full two points. Good luck and have fun!