Many people I meet have read books by Cesar Milan or have watched his TV show, and he talks a lot about dogs trying to dominate their people. Dog trainers who are actually educated in the behavioral sciences have a very different view of this. I'd like to share a bit of that view with you in the form of a position statement on "dominance" from the Association of Pet Dog Trainers, of which I am a professional member.
While dominance is a valid scientific concept, the term "dominance" itself is widely misunderstood, such as when it is used to describe the temperament of a particular dog. Dominance is not a personality trait but a description of a relationship between two or more animals and is related to which animal has access to valued resources such as food, mates, etc. It should not be used in any way to support the belief that dogs are out to "dominate" us, especially as that misunderstanding causes some people to respond with force and aggression. This only serves to create an adversarial relationship filled with miscommunication and even more misunderstanding. The unfortunate result is often anxiety, stress and fear in both dogs and humans towards each other. The use of techniques such as the "alpha roll" on dogs, which is based on these mistaken beliefs about dogs and wolves, has no place in modern dog training and behavior modification. Dogs often respond to this perceived threat with increased fear and aggression, which may serve to make a behavior problem worse and ruin the dog-owner relationship. Read the whole statement (about a page long) here.