Every Sim is some type of stereotype or a deconstruction of a stereotype. I'm interested to see, and maybe even get some inspiration, on what kind of households you put into your worlds; whether as NPC households or ones you play yourself.

I like to have a Femme Fatale-type: 1 (Young) Adult Female Sim, whose clothes and appearance are sex appeal incarnate. Heavy make up, pretty clothes, with at least Flirty and Commitment Issues as traits. Sometimes, I might put her into a bigger, more expensive house. (Paid for by her current sugardaddy/sugardaddies. Or add a Black Widow twist by having it be paid for by her deceased husband's inheritance)
A male version of this would be more Casanova, who Dislikes Children.

The Single Parent household being 1 (Young) Adult Sim and a child, generally of opposite genders. I particularly like to make single dads with a daughter, who has grown up to be a complete tomboy.

A hermit author, who Hates The Outdoors, Loner and is basically designed to be great at writing. Sometimes, I make them a 'shell' house with a basement and the upstairs is completely empty and all the furniture is in the basement, where the Sim is living because they want to avoid seeing people.

Okay, I'll start.

The kleptomaniac couple. Both are mooch and kleptomaniac, one is in politics, the other works as a criminal. When I placed them in my neighborhood, their two children, via Story Progression, became both Insane. Too bad I have a good last name for them.

The backward journalist. I have based this on an Internet meme. Basically, this Sim's way of thinking is better suited for the Middle Ages and gets triggered by every modern trend. But this Sim really wants to work as a journalist so he/she has to deal with it. (Hot-Headed, Neurotic, Inappropriate)

I also used to have the single parent household. But same-sex (father-son, mother-daughter). I then placed them on a small house with a double bed. Imagine how awkward for them when the child became a teen?

I have some families saved to the bin that I like to plop down in saves that don't have enough sims:

- A Chinese family of four, where the parents are ruthless businessmen and hate each other, and the two kids (teen daughter and child son) rely on each other for moral support;
- A white family with Victorian values, with all members possessing the Proper and No Sense of Humor traits;
- A black family with the husband working full-time in the Law Enforcement career and the wife working part-time at the bookstore;
- Two black/white interracial couples with a toddler and another kid on the way;
- A Scandinavian family with 3 kids, with all members possessing the Friendly trait;
- An orphanage, with an elder, a young adult and 6 children of various ages;
- A clan of fairies consisting of a main couple, the elder parents of one of the spouses, and toddler twins of the main couple;
- A single mother or father with a toddler and a child;
- A family with a single child, of whom only the child is a Witch;
- An Evil businessman with a family, who also has a live-in Evil mistress whom he passes off as a secretary.

Aside from the first family, I switch the races and genders around sometimes.
The Chinese family has so far been the most interesting, though: the couple always splits up and the two will usually take turns getting with half the town.
The businessman with the live-in mistress also tends to marry his mistress and throw his wife and/or kids out :/

Edit: I have a few gay couples too, along with a household with 4-5 young adult roommates

I have a similar one, but Japanese. Husband and wife, with her as the demure, soft-spoken one and him the authoritarian. The teen son 'hates' his father because he's so strict, while the younger sister is... well, she's okay. Nothing big with her.

The Outsider: A sim who has recently moved into the outskirts of town and is very different from any of the human neighbors. Sometimes they hide their differences (Or possibly even their presence) from strangers as much as possible, sometimes (Like my incubus) they flaunt them. (And yes, I had aliens, fairies, demons, etc. ever since the base game. All it requires is a bit of imagination, although mods and cheat codes help with giving them powers.)

Almost in all neighborhoods I ever played, there are two leading rival families; I'm not proud of saying it, but in this I follow the EA pattern - like they put the Altos and the Landgraabs into Sunset Valley, or do you remember the Capps and the Montys in Veronaville? It's the "family feud" stereotype, but it helps me a lot to make the social network of the whole town more dynamic and interesting; in each character's case, it raises the "whose side are you on?" question. In my gameplay, It entertains me how they rival for the highest political or business (or even the top criminal) positions, how they marry for wealth or influence, and how they try to influence their children not to marry someone from the "other side".

A, er, variation on the prosperity challenge - I start with a couple with a large house and no furniture. He's a slob and she's frugal. Neither is allowed regular jobs. (What she does varies on her other traits, but he's doomed to becoming a professional dumpster diver.)

Crazy cat lady. Or her alter ego, the loner who loves his dogs.

A redneck challenge family (adapted from Sims 2, where it's harder - it's entirely too easy to make money in Sims 3) - their traits vary, but high-paying jobs, college, and "ambitious" or "workaholic" are out of the question. They live in a double-wide - if they're lucky.

Current favorite families to plop down when there's not enough sims in town:

-An elderly household. All of them are elders, of various types. One is a powerful vampire, one is a gold digger, one's...well you get the picture. They don't get along but I force them to stay together with story progression lol. They have a dumb old doggy too, but he's a good boy.
-Immature adult, with a good and klepto child. Mother tries to be a successful artist but fails terribly since she has so many enemies, so the kid has taken to stealing to pay for groceries.
-Single dad with a household of kids. Dad is a workaholic.
-Three teens who all ran off together. They live in a tiny starter house and have super cheap...everything. In my current game two of them are dating.

I almost always make the grumpy professor dad with his two daughters. I gave him the dislikes children trait bc it's an accurate depiction of my teachers ;P

Then I make the big brother who takes care of his little sister, their parents dead.

The immortal vampire escort who loves their job.

Creepy stalker guy/girl & their serial killer lover (cringe I know but why the hell not)

A typical roomies household

An orphanage with a terrible caretaker. The caretaker ends up assassinated by one of the kids... who also becomes heir to the town serial killer.

I've only recently figured out that it might be a good idea to populate my worlds with "background" characters. I had one of those households already, but they eventually became too interesting.
These ones didn't. Meet the Mahara family.

From left to right: Oliver Mahara, Stace Mahara, Colonial Mailbox Mahara, Jamille Mahara, Trenton Mahara, and Elliott Mahara. They're all completely unremarkable. Sure, one of them is a mailbox and Elliot is a bit of a weirdo, but there is nothing remotely unique about them besides that.

And before I forget; Bridgeport 1988 resident and @gittevdv creation, Anouk Beachey. Anouk is also pretty unremarkable but much like Elliott, she won't be for long.

Had a similar one. Teen brother and sister, living with their toddler sibling. Background idea was that mom died giving birth to the youngest and dad ran off because he was too stricken with grief to care for anyone else anymore.

Similar idea with a father whose wife died after giving birth to twins and he has to raise them on his own now.

The Rich Elderly. Basically an elderly Sim couple that I use cheats on to fulfill their lifetime wish immediately upon moving them in. Not only makes them super happy, but also gives them money and I can make them count as 'rich' in the game. (Which is at 25.000§, right?)