In the first of many episodes to explore Jan's middle child insecurity, Jan gets a mystery locket in the mail and much of the episode is about her trying to find out her admirer is. At the end it turns out to be Alice, a middle child herself who understands Jan's insecurities all too well and wanted to give her that feeling of being special. Jan's response? "As long as I have this locket, I'll always feel like someone special".
A similar incident happens with Bobby pretends to be a secret admirer for Cindy, who wishes she were older and more glamorous. When Cindy wants to meet the guy, he offers his friend a half-dollar to play the part of the admirer...only for the kid to fall for Cindy for real and give Bobby back his money.
On the pilot episode, Mike notices that the photo of the boys' birth mother is missing from the dresser. Bobby admits that he put it away because he didn't think Carol would want to see it. Mike tells him to put it back. "I don't want you to forget your mother, and neither does Carol."
In the first season Marcia writes a letter to a local newspaper saying why her new stepfather should get their "Father of the Year" award. In order to secretly mail it she sneaks out of the house past curfew. She gets caught and Mike has to punish her by not allowing her to go with the family on a ski trip. The newspaper picks Mike based on Marcia's letter and a TV crew goes to the house to surprise him and present his award. That's when Mike discovers why Marcia snuck out of the house. He reads Marcia's letter "Even though he's been my dad for a short time, no father could be a realer father than Michael Brady." Mike then hugs Marcia.
In the 3rd season, Mike's anniversary present to Carol is a professional photo of the kids together. Unfortunately, Jan ruins it by crashing her bike into it and the kids have to go out and get a new one without their dad finding out. They succeed, but afterwards Mike corners Jan and tells her he knows something happened because she's wearing her glasses in the new photo; when she tells him the whole story he tries to ground her from riding her bike, but Jan says that won't work because she already sold her bike to pay for the new picture. Mike is so blown over by her integrity that he decides not to punish her and promises to get her bike back.
In "54-40 and Fight", the kids come into unexpected Checker Trading Stamp gold when Alice offers her collection. The boys want a rowboat, the girls want a sewing machine and ultimately they end up building a house of cards to determine the winner of a whopping 94 books of stamps. The girls win, but after seeing a rowboat near the sewing machines at the redemption center they feel bad for the boys, and instead pick out something the whole family can enjoy: A color TV set.
I'm surprised no one's mentioned the episode Every Boy Does It Once, when Bobby decides to run away because he's just a "stepchild". The most heartwarming part is where Carol offers to run away with him so he wouldn't be alone because "it's a big world out there".
Also, when Carol says "The only 'steps' in this house are the ones leading to your room."
In a real life example, one of the reasons Robert Reed kept staying with the show despite disliking the scripts was because he had grown fond of the cast and treated the children in the cast like they were his own.
Jan runs away from home after one too many instances of Marcia stealing her thunder and ends up hitching a ride with a trucker. After hearing Carol call out for her on the CB radio, she decides to go home where the family finds her asleep in the living room. A warm reunion is had, complete with Jan telling her family how much they mean to her and Marcia finally returning the credit she took for an idea of Jan's.
Jan's psychotic inner voices finally shutting up after Grandma pays her a little attention. Doubles as a Funny Moment when the voices transfer themselves to Cindy.
In the second movie, Jan finally getting the boyfriend she's always wanted (who's just as Adorkable as she is) and Marcia genuinely being happy for her after playing the bitchy older sister for the whole movie.
Cindy giving her doll to the millionaire after realizing she doesn't need it as her security item anymore.
Peter realizing his father's been his best role model all along, after realizing what a dick "Roy Martin" is.