It's pretty well known that yawning is contagious. If you see someone yawn, you are more likely to yawn. This phenomena is poorly understood, but it's thought to have developed as a result of increased primate nonverbal communication - signaling boredom or tiredness. It also may underly empathy; autistic children, who exhibit blunted social awareness and empathy, do not experience contagious yawning. Humans "catch" yawns from one another, from chimps and other primates, and vice versa. A recent study suggests that dogs can catch yawns from humans. This blog post covers the paper in more depth. This article has a video of the experiment.
It's unclear whether dogs can catch yawns from other dogs, or only from humans. If only from humans, it suggests that the ability stems from thousands of years of selective breeding for dogs that were better able to read subtle cues in the countenance of their owners.
Obligatory pictures of animals yawning below the fold: