From an outsiders point of view… All In the Family. Sure some of the names and fashions have changed but the same fights and divisions still seem to be there.
Now if they could digitally substitue Bush for Nixon and Iraq for Vietnam…
You’ll have to excuse us, we seem to be caught in a temporal anomaly at the moment. There were a good two decades in there when we weren’t like that, but at the moment, we’re smack in the middle of 1972 again. Everything from fashion to politics to appliance colors is irritatingly seventies right now.
No one of their income level has an apartment that big in NYC.
Seinfeld was more realistic in that regard. Jerry’s apartment was comparatively teensy for a sitcom.
I’ll accept that, although I wasn’t really thinking about the size of their living quarters. I meant more how they lived their lives.
The thing is, though, that the situations and relationships in the show are pretty much the same sort of mundane shit families go through anywhere else. Change the accents and make Hank love the Michigan Wolverines and you could set it in Grand Rapids. Change the accents and change Hank’s adoration to the Red Sox and it could be set in Natick, MA. Change the accents again, make Hank a Giants fan, and whammo, you’re in Los Gatos, CA.
Much the same could be said of “Roseanne,” which was going to be my nominee. That LOOKS like a real family. They worry about paying the electric bill and eat macaroni and cheese. (Kraft Dinner, as I’d call it here in Canada.) The show was about ordinary shit. Hell, have them speak Spanish and it could be The Rosie Gonzalez show, set in east L.A.
Where the Sopranos is different is that it’s about a wealthy crime family where a relative or friend or associate is murdered every couple of weeks. It’s simply not transposable to millions of ordinary families. The Sopranos depicts some of the mundanity of family life, but there’s too much Mob stuff for it to be truly representative of more than 0.1% of the USA, and they’re more dysfunctional than most families, anyway.
I would say The Simpsons, simply because it touches on nearly every aspect of American pop culture. Sure, it’s not based in reality, but after watching a season of that show, you will get a taste of nearly every slice of life in America. Plus, did I mention the constant reference to various aspects of pop culture?
And they live in a mountain town by the ocean in the midwestern part of the southern part of the country with a lake where it snows and they have a baseball team etc. Everyone can identify with their location!
Or maybe Beverly Hills 90210. Hey, at least it keeps the perception alive. 
And have him shake hands with Jerry Ford…maybe in a flashback (instead of George W. Bush).
Wow, almost none of these fit into the “series of the last 10 years or so” stipulation of the OP. I have no suggestions, because none of the ones that I can think of are from the last 10 years either.
Roseanne and Malcolm in the Middle get my votes. Roseanne for the fact that with only slight changes to the family, every single person I know well grew up like that. Their food, their situations, their interactions, everything. Anyone who wants to know how the majority of the US lived 15 years ago need only watch a few episodes.
Malcolm also has very a realistic family dynamic.
Nothing on TV captures the essence of the American spirit so well as professional wrestling.
Unfortunately, anything featuring stupid children of millionaires.
I’m not sure what show best represents America, but this seems like a good time to tell the story of a woman I worked with one summer several years ago. She had just come over from China, and had only ever seen one American T.V. show. Naturally, she assumed this show was representative of American culture in general.
I hope she wasn’t disappointed with our failure to sleep with each other’s spouses, start fistfights, and burst into spontaneous chants of “Jer-ry, Jer-ry!”
3rd Rock From The Sun had some real family things going on in it
Roseanne may not be currently (or recently) in production, it is actively in syndication and available on DVD. The plots of the shows weren’t really time-specific and would be just as relevant if the show were in current production.
Yes. Studying Earthlings and figuring out their own family unit dynamic.
I have to vote for Simpsons, over all.