My dog, yes, my son plays with... and our dog is huge. Our dog doesn't have a mean bone in him, and we reward him by dealing with the baby by letting our baby feed him treats; he's so gentle!
Other dogs, NO NO NO. I don't know other dogs, not even our best friends dogs, the way I know mine. All it takes is that ONE TIME for the dog to be in a cranky mood, and you've got a trauma on your hands. I've always told my kids that unless it's our dog, you stand back, don't approach the dog, and if a dog comes up to you, don't make any sudden movements or loud noises, just stick your hand out low, palm up, and let him sniff you. Don't try to pet another dog.
My 7 year old, when she was 4, got bit by a dog at her dads house; a dog that had a history of being grumpy, but never biting (why they left her alone with that stupid mutt is beyond me, but whatever). My point is, even a dog she'd known for 4 years had noooo problem taking a nice size chunk out of her arm.
I don't worry about this with MY dog, just other dogs. It's always okay to play it safe if you have any indication that the dog may not behave.