Do you just want to know about puppies? or do you plan to keep your pet after it's grown up and not as cute any more? Almost any puppy is great for kids, and of course it depends on what kinds of dog you like too. So if you plan to keep your pet, here are my recommendations...
big dogs: Golden Retriever or Labrador
very friendly with kids even when they're older
medium dogs: Spaniels
very playful -- but they pee when excited
small dogs: Terrier (Yorkie/Westie)
easy to take anywhere
to avoid: American Eskimo, German Shepherd, Pit Bulls ---- these are all pretty cool dogs, and i've owned some that would have been great for a family -- but in general they can have traits that aren't good for kids.
I've owned and trained many dogs (from 8 lbs to 110 lbs, mutts and purebreeds) -- and have close contact with many other dogs at other families. We currently have a mutt (chihuaua/spaniel/terrier) who is absolutely adorable and great with our two kids (both under 2 yrs).