Richard: I don't want to go back to the pool house...
Emily: Then come home.
Rory's high school graduation speech. Even Luke can't hold back tears.
Jackson and Sookie's picnic date, where he proposes.
Sookie: So, I'm sorry, you don't think we should live together anymore?
Jackson: I think we should get married.
Luke and Rory's exchange after Rory and Jess get into a car accident. Everyone, especially Lorelai, spends the episode blaming and deriding Jess, ignoring Rory's promises that the accident wasn't his fault and making Luke hide away from everyone. Then they finally talk to each other.
Rory: "Luke...it wasn't his fault."
Luke: "I know it wasn't."
It's an incredible CMOH, first for the relationship between the two of them: Luke is clearly feeling guilty about Rory's broken arm and worried she'll also blame him and Jess, her comfort is beautifully played. A great moment for Jess too, its obvious both of them do care a lot about him - despite his jerkisness - and the only ones who believe in him.
The entirety of Luke and Lorelai's first date, particularly the revelation that Luke had held on to a humorous horoscope that Lorelai had given him pre-series.
Luke building Lorelai an ice-skating rink.
Luke bringing Lorelai flowers...The first and only women he ever bought flowers for.
Luke and Lorelai first kiss.
Really, Luke and Lorelai throughout Season 5.
At Rory's Bon Voyage Party in the series finale, where she thanks the town and her mom for giving her such a great start in life.
Rory: I don't want to gush, except to my mom, who is everything to me and everything I am. And who I'm gonna miss so much.
And then Lorelai indicating that she'll continue having Friday night dinner with her parents. This shows that after seven seasons of relying on their shared love for Rory to hold their once broken relationship together, it's strong enough to stand on its own.
Rory's impromptu speech at a town meeting about wanting to tell people how they really feel about them, which even gets applause from the townspeople.
Liz and TJ's wedding.
Max delivering a thousand yellow daisies to the Inn after Lorelai offhandedly mentioned that such a gesture would be the right way to propose to her. Then following that up with Lorelai and Rory running through town because they can't wait to share their good news with each other at the end of season one.
The end of The Prodigal Daughter Returns where Rory and Lorelai finally make up after a months-long separation?!
The very last line of an earlier scene in that episode, when Emily is telling Lorelai that Rory has moved out.
Emily: I lost her just like I lost you—it feels remarkably similar to me.
Lorelai: You didn't lose her like you lost me. Rory was never even supposed to be here in the first place. She was always supposed to be at school—she just went back where she belonged. And you didn't lose me.
The looks of pride on Emily and Richard's faces when Lorelai graduates from community college. Heart-warming to the point of being a total tear-jerker.
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.
Jess and Rory's reunion in Season 6. Especially Jess crediting Rory for his success as an author.
"So, I just wanted to show you this, and tell you uh, tell you I couldn't have done it without you."
Especially heartwarming, as last time Rory saw him, Jess was a drop-out and failure.
Jess' Character Development over the series in general, going from said drop-out and delinquent to a mature, hardworking artist who even gets his own books published.
Jess and Luke's hug at the end of Season 4. Followed by this line:
"I'll always be here, Jess."
The whole Season 4 arc with Luke and Jess is pretty heartwarming; climaxing with Jess coming to Liz's wedding because of Luke, and admitting to his uncle he still loves Rory. Luke's unspoken understanding of pining for a Gilmore girl is beautiful.
Lorelai storming into Jason's office to tear him a new one for making her mother feel like shit.
After Luke's speech to Kirk (see Awesome sub-page) when Kirk is talking about breaking up with Lulu, Luke later sees them together. Kirk raises a hand in acknowledgement and puts his arm around Lulu.
Dave read the whole Bible in a single night to prove he was worthy of Lane. Even Mrs. Kim had to admit she was impressed. Also a Crowning Moment of Awesome on Dave's part.
Mrs. Kim giving Lane her grandmother's wedding ring when she gets engaged to Zach.
In season 5, when Dean dumps Rory (the second time) in front of several people at her birthday party, Logan and his friends immediately rush to comfort her and begin trying to cheer her up, offering shoulders to cry on, alcohol.... and reenactments of The Passion of the Christ.
Logan: Hey, Ace, nothing ever seems quite as bad after Finn's Passion of the Christ. ...Except Finn's Passion of the Christ.
Combined with Tear Jerker, Emily and Mia's conversation about teenage Lorelai running away with baby Rory and finding shelter with Mia at the inn. Emily then ultimately asks Mia for photos of young Lorelai.