Seeing that Counterpart has been mentioned twice but no pictures were provided, I decided to include a few:
Counterpart is one of two things that sparked my interest for Go. Unfortunately, I think S01E05 was the last episode to reference the game—incidentally, with a book found in someone’s apartment:
Okay this is quite a stretch, but it’s still good. 
Misaeng, the K-drama (based on a comic). Go is a major part of the protagonist’s plot.
And it’s a great series.
And to carry on with time travel, here’s a match directly from TMNT III (of all things):
They could have at least found someone who knows a little more about the game to set up the stones in a relatively realistic manner … 
Gummy stones??? 
If you don’t mind my posting moving pictures…
Here’s the scene from Counterpart I mentioned before:
And from the movie Pi, referenced by @OnceAhasverus:
Finally, the iconic scene from A Beautiful Mind, mentioned by both @kickaha and @_oopsImStoned:
Aargh… my eyes, my BRAINS. They hurt.
Isn’t that Othello?
My missus is currently watching “Ashes of Love” on Netflix which has scenes of the characters playing Go, despite it being called “Chess” in the englisch subtitles. Unfortunately I could not find any pictures online.
Wow! Strange things indeed. What the hell happens to GO in 2053? Looks like the game has changed a lot. Jeez. I would say it’s not GO anymore, perhaps enough time has passed that it’s GONE instead.
From Rurouni Kenshin: Trust & Betrayal (and game actually looks like it makes sense which is rare enough in movies 
)
From Mobile Suit Gundam: The Origin Episode 2
Another vaguely realistic looking position!
