In all honesty, most big dogs are friendly unless you train them not to be. Labradors, Great Danes, Golden Retrievers, and Mixed Breads all have wonderful personalities.
In my opinion the most popular family dog that is a large breed wuold be a lab, then again alot of big dogs make good family dogs. It depends on the breeder as well as the breed. Labradors, German shepherds are two breeds that come to mind right away.
The obvious choice is a labrador but great danes, which are very very large dogs are very mellow and friendly too. Huskys are hard to come by but they make excellent family dogs.
I had a great dane who thought she was a small dog! Very gentle with kids and was wonderful with my elderly grandmother! My opinion is they are the best big breed!