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.
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
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.
Come on, how has no one mentioned the scene at the end of The Prodigal Daughter Returns where Rory and Lorelai finally make up after a months-long separation?!
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 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.