The three dogs are mostly around to have the nine puppies that Napoleon turns into his private army. (Well, that's the point of two of them, anyway.)
What's weird is that the dogs, who have teeth and strength and all that good stuff (as demonstrated by the nine dogs), don't make any attempt to rebel against the manipulative pigs. Why? They're not aware of their own strength—plus, they also seem to have a somewhat overdeveloped sense of loyalty.
Hm. This seems to be a universal problem on Animal Farm.