Did any Trojans survive the Trojan War?

They were taken home as slaves by their conquerors, or sold locally and the proceeds distributed.

There is a 1st Century BCE story (a thousand years later) that Aeneas was able to flee Troy as it was being sacked, along with a small group of people (in the movie Troy, at the end you see Aeneas with his father on his back, getting out the back gate - setting up the sequel - wait for it). His progeny were supposedly responsible for the founding of Rome. Read The Aeneid. Julius Caesar claimed descent from Aeneas, and therefore descent from Venus who was Aeneas' mother.