Your dog may sometimes show off his oddball side by sitting on other dogs. This is actually fairly common among dogs. The behavior usually starts either because your dog wants to play or because he wants to assert dominance over another pet. Although the behavior may not be harmful, it does bear watching.
Display of Dominance
Dogs show dominance in a variety of different ways. If you notice that your dog insists on eating first, leading on walks and having first choice of the toys, his sitting on other dogs is likely just another example of dominant behavior.
When your dog sits on another dog, he may simply be playing. If he is, you'll see it in his overall demeanor. His hackles won't be raised, his ears will lay flat, and he won't sound menacing growls. A dog who wants to play will hold his tail in relaxed position or wag his tail rather than pointing it up or straight out. It may not be unusual to see your dog call an end to the play session by sitting on the other pet.
Training Other Dogs
If your dog is older and you recently introduced a younger dog to the household, he may be training the younger dog in acceptable behaviors. Young dogs, especially those still in the puppy stage, can be extremely rambunctious. This is enough to aggravate an older pet who is probably much more interested in napping than in constant wild play sessions. Your older dog may be issuing a gentle correction to the younger one. You may notice that the behavior stops once the young pup learns the limits.
When It's a Problem
This behavior can become a serious problem if you have a large dog who insists on sitting on a much smaller animal. For example, a 70-pound greyhound sitting on a 5-pound toy poodle could cause injuries. This behavior needs to be discouraged. Separate the two dogs when you're unable to directly supervise. Firmly issue an immediate verbal correction if you witness one dog sitting on the other and lead the offender away. If you are unable to solve the problem with these methods, consult your veterinarian or an animal behaviorist for help.