Once again Brewery Ommegang has released a special "Game of Thrones"-inspired beer, and the Three Eyed Raven is a dark saison that mixes the fruit and spice character of a farmhouse ale with a roasty dark beer. It's an interesting mash-up of styles, and you could make a case for a special brew like it being served at a royal feast in the fantastical realm of Westeros.
But what other types of beer could be filling the drinking horns of the (anti)heroes and (sympathetic) villains? Looking to the novels for clues doesn't yield much. While author George R.R. Martin describes the wines of the realm in great detail, beer gets mentioned mostly in passing.
AleSmith Brewing — Nut Brown. A classic English-style brown ale, Nut Brown has a round and rich malt body with a fruity yeast character and that distinct earthy finish from English hops. It's particularly vibrant when brewery-fresh.