In most games of skill, some moves "feel right" or "look good" to good players, and part of becoming a better player is acquiring the instincts that make better moves feel better. This is certainly true in go; you need to feel "no, black shouldn't play there, because it makes his stones overconcentrated in that area" or "white should do that, because the shape it makes is beautiful" in a lot of situations. It's partly pattern recognition, and partly developing somewhat-quantitative strategic instincts.

(Be cautious about believing anything I say too much. I'm a pretty weak player.)

One thing I like about go is that even a beginner like me can follow an expert game. Although I’m many orders of magnitude from being able to generate it, I can appreciate (“verify”) the quality of play in http://senseis.xmp.net/?FamousGoGames . I’m not sure that’s as true of something like chess or Scrabble, which seem to get abstruse and memorization-based at high levels.

Go has a kind of deceptive shallowness. The rules are extremely simple[0]. You can see 90% of what’s going on on a given board in a few seconds. (The board looks like a simplified illustration of something else – like the phase portrait of an uglier game.) Another beginner and I can play a game that looks roughly like a game between masters, and with a heavy enough handicap we can even play a satisfying game with them.

What’s fascinating and addictive is that there’s no big secret. Learning go, for me, is reminding myself that it’s simpler than it looks. All I have to do is surround territory. It’s very, very hard. The last 10% of understanding a board takes decades.

0. The Tromp-Taylor rules, which you mentioned and serve as an excellent introduction for the curious hacker, are at http://homepages.cwi.nl/~tromp/go.html . Notice the 150-line Haskell version.