'Dawn of the Dead'
In the 2004 remake of George Romero's classic zombie apocalypse gore fest, a band of survivors holes up in a shopping mall besieged by the living dead. Chips the dog appears about halfway through the movie, when the survivors find him in an underground parking garage. He ends up driving a major part of the plot when everyone realizes the zombies ignore dogs and only attack humans. They send Chips on a mission to deliver food to their friend Andy in another building, but the zombies gain entrance through the dog door and attack Andy. One of the survivors, Nicole, has become very attached to Chips, so she uses a truck to attempt a rescue. This drives the rest of the team to rescue Nicole in turn.
Despite being in serious jeopardy (along with everyone else), Chips is never harmed by any zombies and accompanies the survivors on all their travels after they find him. He's with them at the film's end, on the boat. The credits sequences suggest he runs off on an island overrun by zombies, who will presumably ignore him.