Friends/Heartwarming

The episode where Ross accidentally breaks a little girl scout's leg. To make up for it, he attempts to sell as many of her Girl Scout cookies as possible so that she can go to space camp. When he fails to sell the most cookies, he, Joey and Chandler set up their own "space camp" in their apartment especially for the girl. The look on her face as they pretend to launch her into space is too adorable for words.
- From the same episode, Phoebe reacts with horror at Joey's new job where the old dieing Christmas trees are tossed into the chipper if they're not sold. At the end of the episode Phoebe is surprised to find all the remaining old trees have been bought by the Friends and now reside in Monica's apartment, ready to fulfill their Christmas destiny.

Chandler: It's like, "The Night of the Living Dead Christmas Trees".

In season 2 when Rachel tells Monica why she doesn't like her hanging out with Julie.

Rachel: You don't get it. It's bad enough that she's stolen the guy who might actually be the person that I am supposed to be with, but now, she's actually, but now she's actually stealing you.
Monica: Me? What are you talking about? Nobody could steal me from you. I mean, just because I'm friends with her doesn't make me any less friends with you. I mean, you're my... We're, we're... Oh, I love you.
Rachel: I love you too. (They hug)
Phoebe: You guys, um, I know that this really doesn't have anything to do with me, but, um, I love you guys too! (Phoebe gets in the hug) Oh, I really needed that.

The gang singing "The Lion Sleeps Tonight" to get Marcel the monkey's attention.
- In the next episode, Ross wants to spend time with Marcel, but the monkey is being kept to busy by the trainer and for the movie shoot. Ross feels down about it, but at the coffee shop, he looks over and sees Marcel knocking on a window. The little monkey ran off to spend time with him on his own. Awww...
Ross being assured by his father that he will be a great dad.

Jack: You sure you don't want to go to Williamsburg?
Ross: We can go to Williamsburg.
Jack: Eat your fish.

In season ten, a wacky misunderstanding leads Erica, the woman from whom Chandler and Monica are hoping to adopt, to reject them because they lied to her about being the couple she chose. Chandler appeals to her in private and promises that he'll learn to be a good father, but says Monica is already "a mother... without a child" and convinces her to trust them to be good parents. She does, and they end up adopting her twins.
Many fans disliked the Joey/Rachel pairing, but it was still pretty sweet when he realized he was falling for her: she cuddles on his lap as they watch Cujo and asks "Aren't you scared?!" Meaning something else entirely, he quietly replies "Terrified."
- And then when he finally confesses her love to her, it starts out funny when she thinks he's kidding or talking to someone behind her, but it gets sad when she gently rejects him and they hug for so long that onlookers think one of them is dying. They later end up dating for a short time, but the writers realized it was terrible and hurriedly broke them up.
Monica and Chandler's proposals to each other (yeah, that's right) were pretty wonderful:

Monica: In all my life, I never thought I would be so lucky as to fall in love with my best...[crying] my best...there's a reason why girls don't do this!!

Chandler: Okay! Okay! [he kneels down along with her] Oh God, I thought... [he starts to cry too] Wait a minute, I-I can do this. ...I thought that it mattered what I said or where I said it. Then I realized the only thing that matters is that you...you make me happier than I ever thought I could be. And if you’ll let me, I will spend the rest of my life trying to make you feel the same way. [he opens the ring box] Monica, will you marry me?

Monica: Yes.

- Note: Troper is not crying typing this out.
- Heck, the episode was so heartwarming that the writers decided to completely ditch the usual zany antics and Laugh Track of the credits-scene, in favour of having them dance to Eric Clapton's "You Look Wonderful Tonight". It's as beautiful as it sounds.
Many scenes related to the birth of Rachel and Ross' daughter Emma in season eight are very sweet, especially when she tells the doctor to write "Baby Girl Geller-Green" on the form and she and Ross share a sweet kiss.
Season 4 when Ross made both Chandler & Joey his best men.

Ross: I want you both up there with me. You guys are my best... Other guys would be lucky to have just one...
Chandler: Thanks, man.
Joey: I gotta go look at something. (walks away to a corner)

Ross: What a baby.

Chandler: Total wuss. (they both turn away and start wiping the tears from their eyes)

Episode 2 when Rachel returned her ring to pre-Character Derailment Barry. He was composed and civilized and showed no resentment with what she did to him.
Season 4. Early on in her pregnancy, Phoebe freaks out because she's having cravings for meat comes to the logical conclusion that it's what the baby needs. She's very upset at the prospect of killing even *more* animals -- and so, Joey promises to become a vegetarian until Phoebe stops eating meat. *sniffle*
Monica insists that she's not high maintenance.

Chandler: So, they can say that you're high maintenance, but it's okay, because I like … maintaining you

In season two, there is an episode where Mr Heckles dies. (The man who live below Monica and Rachel and was always complaining about the noise.) After they go down to his apartment to collect the stuff he left to them, Chandler is last out. He leans Mr Heckles broom against the door, turns the lights off and says "Goodbye Mr Heckles, we'll try to keep it down." Then quietly leaves.
The One Where Everyone Finds Out-a series of Xanatos Roulettes culminates in Chandler and Phoebe trying to out-seduce each other. They're kissing in an utterly hilarious and the most awkward manner when Chandler breaks it off.

Chandler: I can't do this!
Phoebe: And why not?
Chandler: Because I'm in love with Monica! I love Monica, I love her.

- It loses something in writing, but it's such a good conclusion to one of the shows greatest plots.
I am shocked no one has thought to mention Carol and Susan's wedding, with Ross walking Carol down the aisle when her father disapproves of her lesbianism. And the subsequent dance with Susan, a woman he up until that point (and again from then on) all but hated.
When Joey takes the cooking class with Monica and actually succeeds at making cookies. When the teacher praises him for it, you could tell from the look on his face how much he appreciates finally excelling something at school

Joey: I get an A? In school? Hey, I'm a dork!

Monica and Chandler's wedding, all of it especially Chandler's vows to Monica given that he almost had cold feet.
I can't believe this one isn't on the list yet; it should have been at the top somewhere. In "TOW all the Poker" Ross lets Rachel win because he twooly wuvs her. Aww nothing beats that! It's all the more meaningful in this episode, which pitted the three girls against the three guys. Especially this last game, in which everyone held stakes. They'd spent the whole episode snarking, and trading barbs (well the girls anyway, since they kept losing. In all fairness, they'd just started learning the game.) But, in the end, when it's just Ross Vs Rachel, and Rachel's all upset because she didn't get a job she wanted, Ross throws his hand. And the look on his face, as he watches the girls celebrating... awwww.

Joey: [to Ross]: Ahhh, that's alright. Y'know, that's a tough hand to beat.
Chandler: [to Ross]: I thought we had them!
Ross: Oh, well, when you don't have the cards, you don't have the cards, you know. (looks at Rachel) But, uh... look how happy she is. (smiles)
(Chandler and Joey look at her, and then look back at him. They dive for Ross's hand to see what he had, and he tries to stop them from looking.)

The end of the season 10 Thanksgiving episode. Monica and Chandler don't want to host Thanksgiving because of all the stress they were under while waiting to see if someone would pick them to adopt. They host it anyway, and work hard to make it even better than last year - and everyone else shows up late. Monica won't let them in, Joey gets his head caught in the door, and he crashes into the table and ruins all the food when they manage to pull the chain out. Monica comes back from answering a phone call, sees the mess, and says "I don't care."

Chandler: What's going on?
Monica: That was the adoption agency.
Chandler: And?
Monica: We're getting a baby!
Chandler: Are you serious?!
(They hug, and everyone else joins them, celebrating)

In "The One with the Lottery," following breaking the wish-bone, Joey makes a wish. As lottery madness ensues, Chandler is waiting to hear about a job offer. He doesn't get it, but instead a much better one. Joey takes him aside and thinks he had a hand in it, saying he used his wish for Chandler.
Throughout "The One With the Birth," Ross and Susan are arguing more than ever and over the soon-to-be-born baby. They continue even when locked in a janitor's closet. Phoebe happens to be in tow and makes an observation.

Phoebe: This is so great.
Ross: You wanna explain that?
Phoebe: I mean, well, cause when I was growing up, you know my dad left and my mother died and my stepfather went to jail, so I barely had enough pieces of parents to make one whole one. And here's this little baby who has like three whole parents who care about it so much that they're fighting over who gets to love it the most. And it's not even born yet. It's just, it's just the luckiest baby in the whole world. (beat) I'm sorry, you were fighting.

A small moment from "The One The Morning After": when Monica and Phoebe try a new leg waxing method, it ends up being very painful. Hearing their screams, Joey and Chandler rush in the room with a pan and a tea kettle, thinking they have to rescue them.
During The One With a Chick and a Duck, Ross is supposed to be part of a Discovery Channel panel. Earlier that day Rachel broke a rib and attempted to write it off as no big deal. While Rachel was getting ready to go, Ross saw how much pain she was in, and decided to skip the panel to take her to the hospital.
From the finale, five simple words:

Rachel: I got off the plane.

Ross giving Phoebe a bike after learning she never got one during her childhood. And then teaching her to ride it.
- To be fair, being that Phoebe has a Dark and Troubled Past, she tends to be on the receiving end of these fairly often. It never gets old.