Catan was my first German-style board game[0]. I've since "graduated" on to more complicated games, so I rarely play it anymore, but I find that it's an effective "gateway" German-style board game. Almost all of my friends who have played it love it, and have gone on to try (and enjoy) other German-style games. Catan is nice because it's sufficiently more complex (and well-designed) than Monopoly so as to be interest…
Usually, the algorithms do stuff like:
- if there's a 6 and 8 next to each other, the third field is always a 2 or 12
- there's always wood next to clay
- a 2:1 harbor is never next to a huge field of one type of resource (say, 2-3 grassland)
- etc.