"The Prodigal Daughter Returns" where Lorelai and Rory finally reconcile. Especially when you consider that Rory's spent the whole episode getting her life back together (talking to her dean, moving out of her grandparents' house, parking herself at the Stamford Gazette until she's given a job) and doesn't call her mom and ask to come home until she's completely got herself back on track doubles as a Crowning Moment of Heartwarming
In "Let Me Hear Your Balalaikas Ringing Out" when Lorelai breaks down about how she feels she fails as a mother because of Rory dropping out of Yale and moving in with her grandparents and their subsequent estrangement, while caring for a sick Paul Anka
The scene between Luke and Jess at the end of 'Teach Me Tonight'. Jess and Rory get into a car accident, leading to Rory breaking her arm and a massive fight between Lorelai and Luke. Luke finds Jess smoking on the bridge, where he sat with Rory during the basket festival, on the verge of tears and sits down beside him.
Jess: "I...I made sure she was ok."
Luke: "I know you did."
Rory's graduation speech
Rory : Richard and Emily Gilmore are kind, decent unfailingly generous people. They are my twin pillars without whom I could not stand. But my ultimate inspiration comes from my best friend. The dazzling woman from whom I received my name and my life's blood; Lorelai Gilmore. My mother never gave me any idea that I couldn't do whatever I wanted to do or be whomever I wanted to be...As she guided me through these incredible 18 years, I don't think she ever realized that the person I most wanted to be was her. (tearfully) Thank you, Mom. You are my guide post for everything.
The season three premiere where Lorelai finally breaks down about Christopher leaving her and Rory to go back to his pregnant girlfriend Sherry, because He doesn't want to abandon another child. Lorelai's confessing to Luke about how much Chris's abandonment stings, because he's finally gotten himself together, but it's for another woman and child, is just gut-wrenching.
Rory showing Emily the converted tool shed that she Lorelai used to live in before they bought their house, and Emily realizing that her daughter would have rather lived in squalor than with her own parents.
Emily (to Lorelai): You would have lived in the street, in the gutter, in a cardboard box, anywhere as long as you didn't have to be near us, isn't that true?!
Emily: Richard Gilmore, there may be many things happening in this hospital tonight, but your dying is not one of them.
Emily: No! I did not sign on to your dying. And it is not going to happen. Not tonight, not for a very long time. In fact, I demand to go first. Do I make myself clear?
Richard: Yes, Emily. You may go first.
Lorelai finding out about Richard being hospitalized in the diner and the subsequent freak-out are heartbreaking, as is her conversation with Luke in the car about how she has no real happy special memories with her father, and finally her breakdown outside Richard's hospital room after he turns out to be fine.
Rory and Jess's final goodbye in Season 6. After they kiss, Rory decides to stay faithful to Logan, and leaves. Jess's expression is heartbreaking.
Jess: I guess I'll call Matthew's poet, and have him explain love to me. Poets know all about it, right?
Rory: They're supposed to. I'm so sorry I came here.
Hell, both their expressions are heartbreaking. After everything they went through, its a tragic ending.
Even worse, remembering that Rory ran away after their first kiss as well.
When Lorelai graduates from community college, Richard and Emily are obviously deeply moved and very proud. Their sheer joy and emotion is very touching. This scene is also Crowning Moment of Heartwarming. However, Rory's missing this moment seriously clouds the happy picture.