People who wonder why dogs chase cars are missing the real question – what would a dog do if he caught the car? Finding the answer will satisfy both questions.
Dogs chase cars for the same reasons they chase kids on bikes, cats, small animals and other dogs: They are either playing a game or they are hunting. To a greater or lesser degree, chasing involves a dog's natural prey drive.
In most socialized, well-adjusted dogs, prey drive expresses itself as a canine tag game, in which the dogs take turns being "it." The object isn't necessarily to catch the other dog; the real fun is just running around. Chasing balls or Frisbees is another outlet for dogs' prey drive.
Dogs may play-fight as part of the game of tag, lunging or even snapping playfully at one another during the chase. This form of play may extend to include cats, joggers, people riding on bicycles or skateboards, or cars. The intent is not to hurt or kill, but to engage the other creature (or thing) in a game.
A more serious form of chasing is the hunt. Some dogs have a higher prey drive than others. Sporting, herding dogs, terriers, and hounds have enhanced prey drive; they have the potential to chase and kill their prey. The sequence involves searching, stalking, chasing, catching, biting, killing and eating. Such dangerous behavior is called predatory aggression, but it's not a disorder or and is not engaged in out of anger. It's a natural behavior that's triggered by movement.
Predatory aggression has few warning signs. The dog slides up to the intended victim silently until it is within range, and then launches the attack – nipping at heels, biting, hanging on in an attempt to drag the victim to the ground. The consequences of such an attack can be deadly to the victim.
If your dog shows a heightened prey drive, he should be under your control at all times for his own safety and for the safety of the general public. He may need to undergo behavior modification as well. For more information see the article on predatory aggression.