I'm putting this under kids and dogs because while living with a rude dog is a PITA without kids, its essentially impossible with a baby in the house, and I would venture to say, one of the main reasons dogs get banished to the outside or worse when baby comes.

So the following is a list of what I call "manners" that in my oh so humble opinion, ALL dogs should know, whether they are obedience titled out the wazoo or professional couch potatoes.

Sit, down, stay and come are no-brainers. But need to be proofed in all sorts of situations. Honestly I have to laugh a little at obedience tests sometimes. In my life I never find myself needing the dog to come when he is in a sit stay 10 feet away awaiting my command. I'm hollering "come" when I'm already 10 minutes late to an appointment, and the dogs have found a good stash of deer poop to sample 300 feet away in the front pasture, and I need everyone in their places NOW so I can load up and go already!
Same thing with stay - I'm never asking for a stay when the dog is already in an attentive heel at my side. My stays get yelled out to four dogs rushing in to investigate kitchen mayhem when a knife or glass gets dropped and poses a real hazard to life and limb.
By all means go ahead and teach those commands in traditional settings, but make sure to proof them in the real world. You really don't want to wait until your furry darling knocks over dear, elderly aunt Velma to find out that the sit he does in puppy class so well may not be as proofed as you thought.

Now to the commands you don't necessarily see in obedience rings, but are must have for the well mannered family dog.

WAIT.
Wait is a threshold command. Its what you say when you open the front door, the car door, the gate to the yard etc. It keeps kids from being trampled in doorways, keeps dogs from being turned loose on busy roads when excited kids open doors without thinking. Its a great command. We teach it by opening the door in increments. Dog moves, door closes. The reward is getting through the door so usually no treats needed to teach "wait", but they don't hurt either.

BACK.
Back means exactly what it is - back up. When four dogs are gathered at the bathroom door, ecstatic that you made it out alive, you may find your progress forward totally blocked. Employ the "back" command. One of the four will start backing up and make a spot for you to move through. Easy enough to teach by just moving in to the dog's space and saying "back" as they back away. Praise lavishly, treat, rinse and repeat. The eventual goal is a "back" that does not require movement on your part.

OUT.
An extension of back, that now means completely remove yourself from whatever room you are in. Namely the kitchen but also useful when the human kiddos have a whole horse farm/dragon war set up on the floor of the playroom and thunderfeet decide to come investigate. A quick "out" can save toy horses and toy soldiers until you step on them later barefoot in the middle of the night.

Most puppy classes now also teach a place command, drop, leave it, and general handling by strangers. Also excellent for dogs to have. Again they need to be proofed in real-life scenarios though. Most of the time its not the random pile of poop on the sidewalk I need my furballs to "leave it", its the full bowl of buttered pop corn sitting on the floor between the kids on movie night when they still want the dogs snuggling them. Doesn't make for much of a movie night if you're scolding "leave it" every two minutes. (If you ARE doing this, try the out or place command and make a mental note to work on leave it more )

Added up, sit, stay, down, come, wait, back, out, place, drop, leave it, PLUS walk on a loose leash, greet dogs and people politely AND stay out of the kitty cookies seems like a daunting task for a busy family, but it IS doable! Don't think in terms of finding time in a busy day to fit training in. Instead make training part of your busy day. Incorporate it in to the day.
Ask for sits and downs while waiting for dinner to cook. I like doing doggy torture too and line up cheese or hotdogs on the counter edge and practice leave its.
Practice wait every time pup/dog wants in or out.
Practice place or out during family meals.
Play catch with the kids in the yard and add some come practice with the dog too. Come works extra well if you say come then run away getting the pup to chase you.
Doing laundry? Practice back as you go from laundry basket to drawers/closet. Throw in a stay or two or a game of tug with a drop command here and there.
Reading bedtime stories? Practice stay, settle, or place command.

Mannerly dogs are a joy to be around and fit in nicely in any situation. Definitely worth the small amount of work put in in the beginning and the even smaller effort to keep things sharp.