The Big Bang Theory/Heartwarming

Season One

• Penny coercing the guys to give Leonard a birthday party, and later gives him a birthday kiss as a consolation for the fact he missed it all.

Season Two

• In "The Bath Item Gift Hypothesis", Penny giving Sheldon Leonard Nimoy's Napkin. It's autographed, but she apologized because Leonard (Nimoy, that is) "wiped his mouth with it", prompting Sheldon to give her about 20 different baskets of fancy toiletries. When she says "SHELDON...!", he can only say, "I know, it's not enough is it?"
  • The hug after this. "It's a Saturnalia Miracle!"
• "The Vegas Renormalization." Sheldon is locked out of the apartment with the others in Las Vegas, and has to stay with Penny. After a night full of his usual unreasonable demands, he surprises her and everyone by sincerely thanking her for letting him stay. It's not much, but coming from Sheldon it's remarkably touching.
• "The Financial Permeability" could count for two: Leonard convinces Penny's ex to pay back the money he owes her (humiliating Leonard in the process. The first case of heartwarming is when Leonard allows Penny to get back together with her ex without saying anything, and the second is when Sheldon praises Leonard for such an act of selflessness...

Sheldon: The true hero doesn't seek adulation, he fights for what is right simply because it's his nature...I was wrong. Minstrels will write songs about you.
There once was a brave lad named Leonard, fi fi fiddle dee dee. He faced a fearsome giant, when Raj just wanted to pee...

• Despite being a general tear jerking and heart breaking episode "The Maternal Capacitance" has one heart warming bit. It is of cause how Sheldon and Leonard's mother hit it off, feeling comfortable around each other and ultimately play a game together really gives a soft inner core to what is a really harsh and heart breaking episode.
• The Cooper-Nowitzki Theorem has a small one.

Ramona: Dr. Cooper, I have to tell you, your friends are holding you back.
Sheldon: I prefer to think of it as I'm pulling them forward.

• In "The Cushion Saturation", when Penny and Leonard get the new, dry-cleaned cushion back for Sheldon, who refuses to sit it in, Leonard tries to shock Sheldon into sitting on the cushion by revealing that the only Thai restaurant that Sheldon will eat from closed several years prior, and Leonard has been buying the food elsewhere. When Sheldon mentions that that can't be true because the food is in containers from the old place, Leonard reveals that he bought 4000 containers from them before they went out of business and has been switching them. While this was Played for Laughs, I found it very heartwarming that Leonard would care enough about Sheldon's feelings to buy 4000 containers from his favorite restaurant to keep him from being crushed that it closed.

Season Three

• Penny gives Leonard the best welcome home gift imaginable.
• Overlooked because the joke is that Sheldon is Comically Missing the Point, but in "The Psychic Vortex" Raj and Sheldon managed to make two (quite hot) female friends with Abby and Martha. While Raj and Abby were making out and Martha hadn't figured out Sheldon's asexuality yet (but still enjoying each others company), she asked if she could stay with Sheldon in his room as the others weren't going anywhere tonight. He, of course, did not know what she was implying but agreed to let her in. As she sat on his bed he said, "Make yourself comfortable, I'll go ahead and sleep in Leonard's room tonight." All things considered, especially since Sheldon generally does not like people in his room, that was quite a gentlemanly thing to do.
• Sheldon recognizing Penny as a close friend when she and Leonard break up.

"I've taken great pains to accommodate for your presence in my life, it would be a shame for it all be a waste."

Season Four

• In "The Cohabitation Formulation", Sheldon is compelled by social norms to give Penny tea over the fact that Leonard has a new girlfriend.

Penny: Oh sweetie, I don't really want tea.
Sheldon: I'm sorry, it's not optional.
[Penny smirks at this.]

• In "The Apology Insufficiency", Sheldon accidentally prevents Howard from gaining security clearance to work on a giant laser, and is visibly guilt-ridden about it and spends the remainder of the episode trying to earn Howard's forgiveness. That in itself is unusual for Sheldon, but the fact that he gives Howard his spot, the 'one point from which his entire universe revolves', just to get the guilt off his chest is legitimately sweet. Even if it only takes Sheldon 94 seconds to change his mind.

Raj: Dude, now you have to forgive him! I haven't cried like this since |Toy Story 3!

• In "The Herb Garden Germination", Howard proposes to Bernadette. She says yes.
• When Sheldon suggests to Amy that they treat their relationship like a malfunctioning computer and restore it to the last point they both agree that it worked after she kisses him while drunk. Rather callous for anyone else, comparing a friendship to a computer, but given that we're discussing Sheldon...
• Given how he normally treats his friends, Sheldon (having accidentally drunk tequila) telling Leonard "I love you so much" was pretty aww-worthy.
• There is this surprising exchange between Penny and Priya:

Priya: Nice of you to come for Howard.
Penny: Well... he's my friend, it's what you do. (starts giggling)
Priya: I'm sorry did I miss something?
Penny: It's just so weird, Howard Wolowitz is my friend.

• In "The Toast Derivation" Sheldon balks at his circle of friends changing things up by having dinner at Raj's place, so he seeks to acquire a new group of friends including Zack, Barry Kripke and Stuart. After a disasterous attempt at a group activity (mostly the new guys ignoring the stuff Sheldon had planned) Sheldon figured that changing his schedule was worth keeping his original group of friends. So he walked to Raj's apartment by himself and he humbly said between knocks on the door "All my friends... all my friends... all my friends."
• Basically all of Amy and Penny's relationships as "besties," but especially in S4E16. The instant Amy learns of Leonard dating Pryia, she rushes over to Penny's apartment to comfort her and trash-talk Pryia, because that's what besties do for each other.

Season Five

• Followed up in "The Russian Rocket Reaction," when Sheldon hugs Wil Wheaton, after Wil gave Sheldon an autographed Wesley Crusher action figure that Sheldon didn't get back in 1995, which started their entire feud.

Penny: Raj?
Raj: Hmm?
Penny: Thank you for being my friend. (hugs him)

• • This exchange subtly paid off later in the season when Penny intervenes to break up Raj's relationship with a Gold Digger. An awkward moment between Penny and Raj, like what happened at the end of Season 4, can lead to both parties being standoffish or reticent to be around one another. Penny feels guilty because she didn't know at the time that she was setting him up with a Gold Digger. Who does Raj go to when he needs to be consoled after the break-up in question? Penny.
• In S05 E05, Howard gets offered to go to the international space station, Bernadette ends up trying to convince him otherwise and even goes behind Howard's back to his mother. She ends up making amends with him and apologises, her reasoning being that she'd be devestated to lose him and that he's her soulmate. To see Howard Wolowitz of all people get someone who cares and loves him that much and doesn't want to lose him is heartwarming.
• Also from S05 E05, Wil Wheaton giving Sheldon a mint condition Wesley Crusher action figure signed "To Sheldon, sorry it took so long. Your pal, Wil Wheaton.", this troper isn't sure if this means Wil Wheaton and Sheldon buried the hatchet and will be friends from now on or not, but it was a really nice gesture on his part.
  • It did. Sheldon hugs him and exclaims "Look everybody! Wil Wheaton is my friend!!" while holding the action figure up in the air. THEN HUGS HIM.
• In episode "The Isolation Permutation" when Amy and Sheldon cuddle despite his favour not for it, cuz he considers her his real close friend and constantly tried to help her through her pain of the issues with Penny/Benedette see in the episode, not even Leonard got that much support in his worst moments earlier on.
• Sheldon finally asks Amy to be his girlfriend. Despite it being in his typical, self-serving, emotionally-detached way, by Sheldon's standards it's awfully sweet and Amy recognizes it as such (at least until she had to abide by the Boo-boos and Ouchies Provision of the Relationship Agreement).
• Sheldon giving Amy the tiara, and Amy's reaction to it. Doubles as a Moment of Adorable.

Penny: You look beautiful!
Amy: I course I do I'm a PRINCESS and this is my Tiara! (kisses Sheldon and bear hugs him)

Sheldon: ...(to Penny) You're right, the tiara was too much.

• A Couple from "The Recombination Hypothesis"-
  • Penny saved one of Leonard's inhalers after they broke up and gives it to him after make-up sex. He later uses that inhaler to try to bluff Sheldon out of divulging his whereabouts.
  • The entire episode was about Leonard figuring out what possible future he has with Penny. The majority of the story was a hypothetical scenario about what would happen if they got back together, which involves them struggling to communicate their feelings to each other and devolving into a purely sexual relationship with no emotional connection. He even says outright that all scenarios that go through his head end badly. Despite all that, his feelings for her are strong enough that he wants to give it another shot.

Penny: Have you thought this through?
Leonard: (nods) Yes and I think we should go anyway.

• • After this episode, you see them trying to take things slow and understand each other better through a relationship "Beta Test," which involved open communication and active attempts to fix the "bugs." It's all really sweet to see them want this to work out, it shows how much they've grown and how much they really do care about each other.
• Sheldon backing Leonard up when he was confronting his childhood bully.

Sheldon: (to Leonard) I platonically love you man.

• Howard's apology to Bernadette in "The Stag Convergence," and everything following it.

Howard: Tell her I'm really sorry. And if she doesn't want to marry me, I get it. But what I really want her to know is the guy that she is really disgusted by is the guy that I'm disgusted by, too. But, that guy doesn't exist anymore; he's gone. And the reason is because of her. So, if this relationship is over, let her know that she made me a better man, and tell her thank you.
Penny: Oh my god, Howard! That's the most beautiful thing I've ever heard. And it came out of you.

• Bernadette's father saying that he misjudged Howard and encouraging him to go into space. Getting that from a prospective father-in-law means a lot.
• The closing segment of the season finale... the whole thing. In the lead up to Howard and Bernadette getting married there had been some tension in the group, especially between Leonard and Penny over a horribly misjudged marriage proposal, but watching Howard's space launch Penny muses in awe that she didn't think he was actually going to go into space and Sheldon says with a tinge of jealousy "Boldly go, Howard Wolowitz." Bernadette and Raj both talk about how scared they are for Howard's safety and hold hands watching it happen. Penny reaches to hold Leonards hand, which noticeably catches him off guard. But the biggest surprise is Sheldon, the poster boy for disliking physical contact, reaching out to grab hold of Amy's hand. Amy's reaction says it all.
  • Special mention goes to Howard getting Bernadette a star-shaped necklace:

Howard: Now, I'll need it back so I can take it to the international space station, so when I get back, I can give you a star that's literally been in space. (Beat) Take that, any guy who's ever bought you anything!

• • How about the Astronomic Zoom that revealed the heart on the top of the building?