I think it depends SO MUCH on the individual dog. If you get a puppy, search for a very high quality breeder that really cares about personality traits.
I grew up with a golden retriever who was the smartest, best dog ever. My Mom has since had 3 goldens and they are all wonderful and gentle around children. Our dog growing up would "babysit" us - and if we started doing dangerous tricks on our bikes, etc - he would try to stop us. Such a cool, caring dog.

I've had several basset hounds that were all great around kids. A couple of the rescues that had been abused were skiddish, but overall I think they make great family dogs.
And now we've got a mini dachshund who is just the coolest little guy. So sweet, so tolerant of ds and his rowdy, 6 year old boy ways. He's also wonderful with our friend's one year old. But I've heard dachshunds are not considered the best "kid friendly" dogs - that's why I think it depends so much more on the individual dog.
There are several breeds I would simply never consider. A lab is one of them. I know people love them (and my Mom currently has two that do find around ds) - but not a breed I would take into my home.