Matthew talking Marilla into keeping Anne, and Marilla buckling down. But Matthew better not stick his oar in!
Oops, he does, by giving Anne her first pretty dress for Christmas. With puffed sleeves, no less!
Gilbert leaving a candy heart on Anne's desk to apologize for the carrots incident.
In Anne of Ingleside, she has a necklace he gave her that looks like a candy heart. This was given to her back in Anne of the Island by Gilbert. She wore it to a party instead of the pearls her boyfriend Roy had given her. Or at least she would have if a misunderstanding hadn't ensued.
Gilbert finding and keeping one of Anne's flowers that she lost at the concert.
Anne and Matthew's last conversation together.
"I'd rather have you than a dozen boys, Anne. Just you remember that."
Anne deciding to stay at Green Gables and teach, because of Marilla going blind.
Not entirely a moment, but Marilla coming to love Anne. If there is a moment here, then it is Marilla finally admitting her love to Anne.
The scene when Anne speaks with Diana's rich Aunt after they accidentally disturbed her in bed. By the time Anne is through with her, that old woman is completely charmed by the girl and requests that Anne visit her because she is amusing, "And at her age, amusing people are a rarity."
Anne of Avonlea
Anne trying and then succeeding in getting through to Anthony Pye.
Anne of the Island
Anne's Heroic BSOD after hearing that Gilbert was dying. Yes, it's cliche. Yes, the monologue where she realizes she was in love with him the whole time is trite. But darnit, seeing the usually-poised Miss Shirley, pride of Avonlea, brought down to a shambles by one slip of the tongue of a child just shows how masterful L.M. is at making us feel what the characters feel.
How about Gil finally getting the girl he patiently waited ten years for?
The poem at the opening of the book that foreshadows the above events from one of Anne's favourite poets, Tennyson.
All precious things, discover'd late,
To those that seek them issue forth,
For love in sequel works with fate,
And draws the veil from hidden worth.
It's one of the most heartwarming excepts ever (It's quoted from Tennyson's The Daydream) and so perfectly exemplifies Anne and Gilbert's relationship in this book.
Anne's House of Dreams
Chapter dedicated to James Matthew's birth
Anne of Ingleside
7 years old Walter walking several miles alone in night to get to home, after he heard that his mother was dying. It turns that Anne was giving birth to Rilla