WOW - well the kids use him for a pony!
With kids under 10 or 12, I strongly recommend one of the herding, herd guarding or non-sporting breeds. Breeds that are of a size for them to hug and cuddle up with but without the dog flattening the child if he rolls over on them are good.
Several of the non-sporting adore racing and playing and can fit on the bed with them without having to buy the kids a king size bed each.
I grew up with Bostons and start competing them in AKC obedience at 9 years old.
Pugs are hoot - just watch the bloodlines as they are running about 60% abnormal on hips and elbows and 11% on patellas.
I have a preference for the herding group for kids as they cling so closely to them and want to watch over them. In that group, there is a smorgasboard of breeds. They go in size from the little guys like Shelties and Corgis to Autralian Shepards to Collies, Belgian Teruvens, Belgian Shepards, and finally Bouvier des Flanders. I would give a miss to Australian Catle Dogs (tend to be nippy), Border Collies (obsessive complusive hyperactives - great performance dogs, tiring as pets), Belgian Malnois (great trackers and police dogs - little too defensive and might take out the kids' playmates). and ditto on the German Shepherd (and we don't even want to go there on their soundness and health prolbems!)
Now Belgian Teruvens, Belgian Sheepdogs and Bouviers have the size since you like the larger breeds although smaller than Mastiffs, are incredibly eager to learn and easy to train, smart as a whip and very, very devoted. (Some Bouviers have a strong prey drive and do Shutzhund but most don't. My vet just got his 3rd for his kids.) They are 3 of my personal favorites for an all around dog - family pet, performance in obedience and tracking, and intimidating potential evil-doers ( and they can take them out if necessary.).
In the working group, herd guarding candidates are the Bernese Mountain Dog (if you can take having a dog that could die somewhere between 4 and 8, typically of cancer); Great Pyreenes and Newfoundlands. Then there is the Kuvasz - ancestor of the Pyreenes and in size, kind of in the middle between the Pyr and a Golden, and still a working herd guarding breed in active use for its purpose. I just placed a 4 year old Kuvasz as the Service Dog for a 4 year old autistic child - his brother has been BOS at Westminster 2 years running and his dam was a Group place winner at Westminster as was his sister - watch the bloodlines on this breed as some are not as flexible and tend to be very guardy (the kid's playmates again) but this dog's particular family has a wonderfully stable temperment and are outgoing and Golden-like friendly but have still swung into action and blocked not-nice people and scared them away - and did it on instinct. Other Kuvs that I know are the family guardian of kids 2 through 8 - the youngest learned to walk hanging on to the dog. This is another breed that will defend its charges and family unto the death. They do not go into comabt easily - first warning, shoving their charges back and away from harm, then blocking the threat from approaching, and then knocking the threat back and away but if forced to go into combat if the threat doesn't get the message, they are one of the few breeds that will self-sacrifice and even dying will stay in the fight to save their charges. The Nazis tried to exterminate the breed because of their "never surrender, fight unto the death" defense of their home and family - and they almost succeeded leaving only 8-10 breedable Kuvasz alive in Hungary at the end of the war.
I would stay away from the guarding dogs in the wroking group. They have a very high prey drive meaning they want to chase and catch and grab. Not so good with the kids' playmates. That would include the Dobe, Giant Schnauzer, Boxers (very strong and hard to persuade that "come" means "come.") The guarding breeds, because of that prey drive, can get a bit too rough in play for kids under 12 or so.
I would stay away from the hounds - unless you enjoy foot races after the dog when he has cleared the 5 ft fence or tunneled out except for one in that group.
The one exception is the Rhodesian Ridgeback. Now they aren't thrilled about playing in the snow - that short coat since they are from Africa. They are in the hound group but they were really a herd guarding who also was used secondarily for hunting. They are incredibly devoted (think velcro dogs), friendly and patient; but let someone threaten their charges and all bets are off. A Rhodesian who had 3 little girls in his charge got the Kennel Ration Hero of the Year when he foiled a pedophile's attempt to kidnap the one child from the bedroom - attacked as the creep who had come in the 2nd story window, was carrying her down the stairs gagged (no bark, no growl just flat out to kill), never touched her and ripped him to shreds. He dropped her and the Rhodie, instead chasing him, put his body over top of the child and woke the household. The police followed the blood and caught him. The canine hero went back to playing with his kids and sleeping on their beds.
(Hmmm..... pretty easy too figure out my top 5 large breeds for watching over home and family but still being a great pet!)
Terriers can be tough in their temperments - fun dogs for romping but they consider "come" to open to negotiation and they'll get back to you.
The sporting breeds are usually high energy. The current popular favorites of Goldens and Labs are sufferring from the effects of being loved too much by too many. Goldens now have the dubious distinction of being the No 1 breed in biting the vet because they are wimps about pain - and then there are the rampant health problems - hips, allergies, a cancer rate in the top 3.....(Love them to death but after 28 years of having them, I gave up because of the way the breed had deteriorated.) The poor Labs are having the same problems now - the hips, etc and I noticed the other day, that the temperment problems must be increasing when I saw the Lab National Breed Club had posted on its breed rescue page "Lab Rescue does not work with aggression. A dog that bites will not be brought into the program." Hmmm... now what brought that on, eh???
Go to the AKC website and read in detail about the breeds
http://www.akc.org/breeds/index.cfm?nav_area=breeds
You can search by Group, Breed name or all of them at once.
Now, when you click on the picture of the dog and go to the page for that breed, on the left is a column. At the bottom of the column, is a link captioned "National Breed Club". Click on it - that takes you to the link to the National Club for that breed that sets the breed standards. The Clubs' websites will give you an ENORMOUS amount of information about the breed - the good, the bad, and the why or why not to get that breed. The clubs websites also have:
(1) a breeders list - all of whom have agreed to abide by the breeders code of ethics (which you can read)
(2) a link to the breed rescue for their breed
Do give serious thought to adopting from an adult from a breed rescue. The clubs' breed rescues go to a great deal of trouble to determine the dog's temperment, personality, likes and dislikes (particularly kids and cats and other dogs in the household), health, and level of training. They make a huge effort to match the right dog to the right home - and if they don't have one they think will be suitable for your home, they won't place it. Great way to avoid the puppy training, newpapers, chewing.......
If you decide to get a puppy so they grow up with the childen, please use one of the breeders who are members of the breed club. A well-bred pet puppy may not be a candidate for the show ring (that nose being 1/8th of an inch to long or something else very picky) but they will be very healthy, the parents carefully screened for hereditary health problems, and from a breeder who has devoted a great deal of time to understanding the breed and bloodlines. A responsible breeder will have a written contract with a health guarantee for hereditary problems; require that if for any reason you ever have to give up the dog that it comes back to them; and always be available for help, assistance and advice about your dog. Such a breeder will tell you if they don't think their breed is right for you based upon your needs. They want a perfect forever home for the puppies - not the money. (In 43 years in the dog show world, I have never known a breeder of that caliber who has made a profit on their dogs - it is labor of love.)
A puppy from such a breeder costs no more - and often less - than from a backyard breeder who doesn't do the health checks, knows nothing about the breed or bloodlines, doesn't give a guarantee, never wants to hear about the puppy again and has breed from mediocre or poor quality dogs.
Sorry for the length - a 2 line answer is facile and there is so much to consider.