This show has many, but one of the most notable occurs in "I Don't Remember Mama", when the Sheffields and Fran sit down to watch old home movies with their deceased mother Sara. Earlier in the episode, Gracie was upset that she couldn't remember her mother, so while watching, she sees her infant self playing with her mother, and Gracie exclaims "I remember that!".
Early in season one's "Here Comes the Brood", C.C. told Gracie that Fran only pretended to love her because of her job. Fran straightened her right out with one of the best speeches ever, all with a charming smile on her face:
Don't forget Fran's conversation, reassuring Gracie that she really does love her:
Fran: It's true: I do get paid to take care of you. But I don't get paid extra for loving you. And I do.
Gracie: I love you too.
Fran: Oh, let's face it, Grace. I'm no Ivana Trump. Of course, neither is she anymore. I got one lousy Christmas club account with maybe 49 cents in it, so I gotta work for a living. Lucky for me, I got the best job in the whole wide world. I love you.
Gracie: So you don't just do it for the money?
Fran: Believe me, by the time they take out state, and federal, and FICA, it's a labor of love.
The sight of Maxwell dancing with Gracie standing on his toes is simply adorable, as Sylvia notes.
Maxwell's proposal to Fran.
Sara appearing to Maxwell on the eve of his wedding to tell him it's okay for him to marry Fran.
More than that, she says she was the reason he even met Fran in the first place. Which immediately shifts to a funny moment.
Maxwell: And you heard her speak? Sarah: I though she had a cold.
Grace's poem to Fran when she thought she was leaving to marry her ex-boyfriend Danny.
Grace: F is for the fun we have together. R is for the rummy that we play. A is for the answers to my questions. N is for the nasal things you say.
I am surprised this hasn't been mentioned yet. When Maxwell decides to have Fran sign the adoption papers, instead of a pre-nup.
In ''Kindervelt Days", Fran is depressed at the prospect of attending a summer camp reunion, so the Sheffield kids sends in her old "Win a date with Eric Estrada" sweepstakes form to cheer her up. Eric actually responds to the form, and offers to be her date to the reunion. However, he has to leave early, so Maxwell steps in as Fran's date.
In "The Butler, the Husband, the Wife and Her Mother", Maxwell and Niles swap roles due to a lie of Fran's mother. Halfway through the charade, the Butlers' Association drops by to make a surprise appraisal of how Niles is doing as a butler. Maxwell and the rest of the household keep up the charade, but of course things eventually fall apart. The Association representatives are getting ready to give Niles a horrible appraisal, when Maxwell points out that if a family is willing put on that kind of performance for their butler, he must be a truly spectacular butler indeed and that Niles is, basically, family.
In the finale, when Fran's father sings "Time After Time" to Fran and Maxwell at their anniversary.
In the episode where Maxwell's brother, Nigel, proposed to Fran and she was leaving the house for what she thought was the last time. She finds Niles sleeping on the couch and she gives him a kiss on the cheek. Considering that he is one of her best friends, I could only imagine sad them saying goodbye would've been had he been awake.
Luckily, she comes back.
Maxwell: Don't you worry, Miss Fine, I've got you.
Fran: Boy, do you ever.
C.C. promises to pay Niles if he escorts her to an event her ex-boyfriend was going to take her to. After their not-date, they dance together, laughing and, for once, legitimately, though still gloriously snarkily, enjoying one another's company. She gives him the check, and he casually rips it up, declaring, "This one's on me," before continuing to dance with her. I think even non Niles/C.C. shippers would agree that was a genuinely sweet scene between the two.
The "The Way We Were" montage in the finale. It's fittingly hilarious and heartwarming in equal measure.