as many have already said, most dogs that bite are a product of their environment. however, there is something to be said for the disposition of a breed—meaning that a dog might be genetically predisposed to certain behaviors that you would need to know how to train it out of…
a pitbull is a great example. we’ve had four in the family. it’s true that it was bread for aggression, but all this really means is that knowing this about the breed allows you to know what to emphasize when training. the key is, ultimately, just to do a lot of research and be prepared for what you’re getting yourself into, whatever the breed.
retrievers are awesome dogs. i’ve had three. they’re great family dogs. very loyal and very unlikely to bite, unless they feel provoked or feel that their family is being threatened (and they will very rarely misread such signals).
overall, i’d say that the most likely to bite are actually smaller dogs with big personalities, like little terriers, for instance. they tend to want to compensate for their size. their bite may not have the same effect as a pitbull’s, but it’s still teeth sinking into skin!
least likely to bite, in my experience, has been portuguese water dogs. my dog now is one, and it just would never occur to him to bite. he was bread to rescue people and to be a companion, so aggression just isn’t in his coding. he’s actually not even aggressive with other dogs or animals. very docile. very sweet… but then again, docility and the accompanying dependancy produce problems too…
Look, the point is that dogs are awesome. Study the breed. Anticipate the negative traits (and every breed has them in one form or another), and train the dog accordingly. Whatever you pick will be rewarding.