Bonanza or The Rifleman
Nothing like a western to scream America!
Or Firefly. If a western screams America, then a western IN SPACE is like, double the screaming.
Supernatural.
Two blue-collar brothers roam the midwest backroads in their classic muscle car, listening to classic rock, eating diner food and sleeping in non-chain motels, hunting down monsters and killing them with pistols, shotguns, big knives and their own bare fists. What can be more American than that?
While some of the topics and areas of conflict might not be as relevant today, I’d still go with All in the Family.
In space, no one can hear you scream!
The Most American TV Show can’t star a foreigner. So no Star Trek, no 24, no Band of Brothers, no Bonanza, no Firefly, no Homicide, no Perry Mason.
Happy Days immediately jumped to mind.
Maybe not todays America but still very American.
Absolutely the answer for me.
I didn’t even need to click on it to know exactly where that link led. 
Hmm, the most American show is probably All in the Family, Three’s Company, American Ninja Warrior, or The Office.
Run episodes of Barney Miller, Star Trek (all incarnations), Big Bang Theory, Dr. Who, Benny Hill, Corner Gas, World Cup highlights, Las Tres Marias, Sandglass and the like. America is immigrants, so what better way to demonstrate that than shows that star non-United Statesians?
Amusingly, all four of those were based on shows from other countries (the English comedies Till Death Do Us Part, Man About the House, and The Office, and the Japanese competition show Sasuke).
For a (near) current series, The Middle and Roseanne might qualify.
Springer.
Friday Night Lights.
Brady Bunch?
Bob’s Burgers
I assume you included Corner Gas as a nod to Canada Day? 
*I’m in Ottawa right now, and it’s hot as blazes! This afternoon, I was woken from a nap by a huge thunderstorm.
Sesame Street