It was easy to lose track of the details in the melee at the end of Game of Thrones' "The Door." A lot was happening all at once, and a lot of it was big stuff: character deaths, history explained, and Hodor. But one major question deserves to be asked: is the Night's King dead on Game of Thrones?
Bran had been relatively safe staying with the Three-Eyed Raven so far, but that all came to an end in tonight's episode. Bran was ousted from his temporary home with a trail of destruction left in his wake. He lost Summer; he lost Hodor; he lost the Three-Eyed Raven; he cost the Children of the Forest their lives. Bran escaped just with Meera, and they're going to have to make their own way in the vast snowy wasteland.
However, just as they were leaving, one of the Children threw some kind of mystical fire bomb at the converging wights. It caused a pretty sizable explosion, and presumably killed everyone inside the cave. However, there's no evidence that it actually took the Night's King down too. Only the wights seemed to be caught in the blast. The Night's King was nowhere to be seen.
The last time the Night's King was spotted in the fighting going on within the cave was when he killed the Three-Eyed Raven. After that, he's conspicuously absent from the rest of the action even though he's ostensibly there to take Bran down. It seems unlikely that the series would get rid of one of its biggest villains without making a huge show of it, and without having one of the main characters be the one to take him out. If the Night's King was dead, you can guarantee the audience would see it happen in full ice-shattering detail.
It seems more likely that Game of Thrones is building up to a bigger climax and saving the good stuff for later down the road. Now that the Night's King is aware of and going after Bran, it will be a threat Bran has to deal with going forward and could end up driving some of his storyline. There is definitely some kind of connection between the two, especially with the Night's King being able to see Bran in a vision, and I would hazard a guess that it's going to mean something big later on – this was just the set up.
Without having explicitly seen the Night's King die, it's a pretty good bet that he's still out there.