When a dog jumps on a human of its own free will, it is not "greeting" the human, it is asserting its dominance over the human; it is the dog communicating that it is alpha and/or wishes to own/control the human. A subordinate would never dream of running over and jumping on the alpha dog of the pack. Space is respect and lower members of the pack respect the higher members. If your dog jumps on humans, it does not respect them. Note: when a young puppy jumps on humans it is sometimes its attempt to reach one's face. Puppies need to be taught not to jump up on humans as this behavior will manifest into other meanings as the puppy grows up into an adult dog.
1. To assert dominance. Whether it's jumping on people or jumping on furniture, both instances illustrate a dog that wants to raise his station in life. By jumping on you or jumping on the couch, he's saying that he's the pack leader--something that you DON'T want to happen, as a dominant dog is much more difficult to train (and can become quite aggressive). In either case, you'll definitely want to institute the proper alpha dog training techniques, if you haven't already.
A relatively new invention that will definitely solve this problem is the no jump harness. It works by restricting the movement of the dog’s hind legs so that it can’t jump at all. This should not be a permanent solution but rather something that can be effectively used during training. It should not only stop them from jumping chain link fences, but also from jumping on people and furniture.
While the idea of "training" may seem daunting, it is simply teaching an animal what behavior works or doesn't work through resulting consequences — so whether you realize it or not, you are actually training your dog every moment of the day. Fortunately for you, preventing jumping is possible even without structured training. There are some simple solutions to this problem that require minimal effort and fit easily into your normal interactions with your dog.
Unless given a command to jump, a dog should never be allowed to jump on humans. A dog that jumps on humans of its own free will is a dog that does not respect the person it is jumping on. Even those cute little toy dogs should not be allowed to jump on people. While you may think it is cute, it is not cute to everyone else. Not only is it annoying to most people to have someone else's dog jump on them, it can also be dangerous. A jumping dog can knock people over, muddy their clothes, put runners in nylons and scratch the skin.