1. The rules of go are very simple. (Well, kinda. Use, say, the Tromp-Taylor ruleset.)
2. The resulting game is very subtle, in e.g. the following senses. (a) For any game, define an "increment" to be how much better you need to be than someone else in order to beat them 75% of the time. Then the number of increments between a total beginner and God is larger for go than for any other game I know of. (b) Same as (a), but this time define an "increment" to be how much better you can get with a week's hard work or something. -- That is, there's a lot to learn, and learning it really makes you appreciably better at the game.
3. The difficulty of the game isn't simply a matter of getting better at mechanical calculations: there's a whole lot of strategy and "good taste" and so on.
4. It seems to be an uncommonly beautiful game. Now, any good game is going to have some aesthetic appeal for its expert players. But it seems as if (a) really good go players get more out of it aesthetically than, say, really good chess players get out of chess, and (b) one starts seeing aesthetic value in the game earlier in the process of getting better than with most other games.
5. (This is, I think, mostly a consequence of #1.) It's a very flexible game: you can use a different size of board (changing how long a game takes and the tactics/strategy balance), or give one player a handicap (changing the balance between the two) while keeping the game substantially the same. This is convenient practically, and (for reasons I can't currently articulate) it seems to me that it indicates something deeper about the game: it's a kind of Platonic essence that can be instantiated in many different ways. (I wonder occasionally about playing go on a graph that isn't just a square grid. It seems like hexagonal go wouldn't be too big a stretch, whereas to make a decent hexagonal chess game you have to change lots and lots of things.)
6. (Related to #1, #4 and #5.) It's a game that can be played with enjoyment even by total beginners: it's much more approachable than chess, for instance.
7. Although there's a lot to learn about the game, the understanding:brute-facts ratio in what you need to learn is better than in, say, chess. You can play go very well while knowing scarcely any detailed opening theory, whereas to be any good at chess you need to learn a lot of lines.