Anime where they play Go?

I'm pretty sure HNG is the only one that revolves around the game.

There is a brief scene in the first season of Code Geass where a couple of soldiers are playing Go. Although, the patterns on the board indicate that either the soldiers are VERY bad players, or the animators were not familiar with the game. Or, I suppose, maybe the rules turned out to be different in the show's alternate universe (bit of fridge brilliance there?).

Also, I seem to recall that Mahoromatic may have shown a Go game very briefly at one point. And I think I saw one more recently as well, but I forget where exactly. It might have been Unlimited Blade Works or Gunslinger Girl.

Interestingly, although Kyon and Itsuki are seen playing a number of different board games in The Melancholy of Haruhi Suzumiya, I'm pretty sure Go is not among them.

Go isn't a very popular theme in Animes. The only one I've seen is Hikaru no Go to be honest. But if you want more of that, I suggest going to Fanfiction.net and reading Hikaru no Go fanfiction! It has a variety of alternate happenings in the Hikaru no Go universe. Example: When Sai leaves and Hikaru is begging to go back in time to when he and Sai first met, there's a fanfiction for that and it was amazing. A lot of them revolve around Hikaru being super awesome at Go so Akira is the one doing the chasing instead of Hikaru chasing Akira. I've even read an amazing one where Hikaru is the reincarnation of Sai with Sai's abilities in Go. It was a very good read.

I hope this helps!