Mom, Dad, 2.4 kids, dog, house in the suburbs. Cat optional.
Basis for most Dom Com series. The name references that this is the minimal "core" family unit, a single generation of parents and kids, as opposed to an "extended" family with cohabiting aunts, uncles, cousins and grandparents. Or the fact that it is usually unstable, can cause hair loss, has a fifty-fifty chance of a spontaneous split, and may also lead to early death; either works. Generally avoided in dramas, as missing parents are a good source of teen angst.
Compare and contrast The Clan, A Boy, a Girl, and a Baby Family, Big Screwed-Up Family.
In the DCU comic Batman and the Outsiders (first run), there was a group of robot super-villain terrorists called the Nuclear Family. They were based on an idealized 1950's sitcom family and had radiation-based powers. They were eventually blown up.
They then got rebuilt for the much-maligned Battle For Bludhaven.
In The Phantom Tollbooth, the main character visits Digitopolis, the land of numbers, and tries to find a way to Infinity. After giving up, he encounters half a boy, cut right down the middle (the other half just not there). Turns out he's the .58 child in 2.58 children for the average family — luckily the average went up a bit, because it was painful being only .47. Fortunately, the average family also has 1.3 automobiles, and since he's the only one who can drive three-tenths of a car, he gets to use it all the time.
''Project NRI": Yamagi Noriko's family is composed of her mother, her father, herself and her little brother Haseo.
The evil supervillain "Brainchild" (a.k.a Charles) from The Tick's animated series is the older son in a nuclear family. His parents are very progressive and hope he'll eventually grow out of the "supervillain" phase.
If you want to break out of the 2-or-3-kids pattern, you could try going much, much larger. This can be justified via religious beliefs note Catholics, Mormons and Orthodox Jews are just a few of the groups whose beliefs promote large families, but it doesn't have to be. However, if the big family is not the main family for the story, it's almost certainly a religious reason — and almost certainly, most or all of the kids are treated as a unit, not as individuals. They may even dress and look identical except for age and gender.
Cheaper by the Dozen (the book, movie version, and modern remake) has 12. In the original movie there's a scene where a representative from Planned Parenthood arrives to ask the mother (who's apparently well known as having her household in order) to head the local chapter... and upon meeting the kids at first thinks it's a boarding school and then gasps in horror, "Why — they're all yours!"
Teresa Bloomingdale's comedy novel I Should Have Seen It Coming When the Rabbit Died is an autobiography about a strongly Catholic family with some 10 kids.
The Carsons in Zilpha Keatley Snyder's The Changeling are like this. Outside of Ivy and Josie, the only one of the eight kids who appears or does anything is Jerry. They're described as all looking pretty much alike.
Live Action TV
The main family in Just the Ten of Us, spinoff from Growing Pains. As Bo-- er, Richard Stabone noted upon seeing the Lubbock family, "They're Catholic!"
Ma and Pa Kettle, stars of a popular franchise of late '40s/early '50s comedies, were a rural farm couple with 15 children. A running gag would have Ma forgetting a kid's name.
Phineas and Ferb, where the family is so blended it can be hard for a casual viewer to notice it at all. This is helped by Ferb, who has a British accent, hardly ever speaking.
Rugrats began with Chuckie being raised by a single father, but in the second movie Chas remarries a woman named Kira who has a daughter named Kimi.
Then again, you could go for moderation:
All-of-a-Kind Family details a depression-era Jewish family with 5 girls spaced two years apart, and, by the end of the first book, a new baby brother.
Live Action TV
Malcolm in the Middle has a core group of three boys, plus older brother Francis (away at military camp, and later starting his own family) and baby brother Jamie.
Or you could stick by the nuclear family, but have the extended family get way more involved than is typical. Instead of a grandparent or two and the occasional uncle or unruly cousin, try adding two to three siblings on each side and two to three kids per sibling (with the childless sibling constantly asked when he or she is going to start a family). Pretty soon you have the kind of setup needed for My Big Fat Greek Wedding.
Anime and Manga
Summer Wars features the exploits of an extended family (and one love interest) over the course of a few days trying to stop a viral social networking disaster from causing IRL mayhem.
In PS238, The Nuclear Family is a superhero team which is also an extended family. Despite their "Nuclear" moniker their power set varies from Gadgeteer Genius to at least one Flying Brick. Student Susie Fusion is the child of one of its members, and Julie Fincher ("84") is the daughter of a non-superpowered offshoot, who doesn't get along well with his superpowered cousins.
The Star Wars Expanded Universe uses the extended family trope quite a bit. In NJO, you might even think Luke and Mara were the Solo kids' parents.
The Western nuclear family is a relatively recent innovation, the product of social and physical mobility brought about by the Enlightenment and Industrial Revolution.
In more traditional societies, like some in Latin America, the Mediterranean, and South/Southeast Asia, this is ubiquitous. Extended family are almost universally considered close family in those cultures. In many of these areas, extended family either lives under one roof or near one another. The Arab Gulf states, for example, are notorious for having cases of three or four generations living under one roof, with all of a particular patriarch's (very fertile) descendants living in a single building. In profound cases (e.g., Italy), "family" might include True Companions, or casual acquaintances.
Weddings are an issue in these cultures. The minimum size for an Indian or Middle Eastern wedding is somewhere in the triple digits; anything smaller and you will run the risk of offending many people. If you live far away from most of your relatives, they will insist that it be held close to them. This goes double if you live abroad—they will have you get married in The Old Country, and that is final.