After Leonard is humiliated by Kurt, Penny's ex. Penny goes over to apologize, and soon degenerates into a crying heap. Leonard consoles her, and they kiss for the first time. Granted, Penny was drunk, but still.
Penny coercing the guys to give Leonard a surprise birthday party, and later gives him a birthday kiss as a consolation for the fact he missed it all.
Penny to Leonard in the last episode of the season: "Yes. I will go out with you."
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." This makes Sheldon realize that he now has a sample of Nimoy's DNA, prompting Sheldon to give her about 20 different baskets of fancy toiletriesnote He had planned to buy every variety of said basket, give her the one that best matched the value of her gift to him and return the rest. When she says "SHELDON...!", he can only say, "I know, it's not enough is it?" The hug after this and Penny's reaction. "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...
Sheldon discovers that Penny is having financial issues and offers her a loan of any size she wants, interest free. He's terrible at being a friend, but it shows that he really does value friendship.
Leonard: You know, Sheldon really doesn't care when you pay him back. It's one of the few eccentricities that doesn't make you want to... you know... kill him.
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.
When Elicia moves into the building and starts stealing the boys away from Penny. In an effort to make them stay friends with her she learns a 'stupid' physicist joke because 'she cares that much', gets them Chinese food and tries to get her geek on, uses a Star Trek metaphor, gets Sheldon's food right from the Chinese food place, and he doesn't even complain about how quickly she got it. It just shows how much Penny really cares about her friends.
The Cat Fight between her and Elicia started because Penny found out Elicia was just using them to do things for her and even had intended to exploit them financially.
"The Adheisive Duck Deficiency": "Sing 'Soft Kitty' for me." Oh Penny, you sly thing, you're lucky that being drugged and a broken shoulder is kind of a sick.
When Leonard is upset at his mother, Sheldon says that his biological family may have abandoned him, but Leonard has "me, your surrogate family". Granted, it's immediately followed by a joke about how unhappy they are about this state of affairs, and Sheldon is a terrible surrogate family member, but the point is, it was a genuine gesture of kindness from Sheldon. He's trying.
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."
In "The Bozeman Reaction", Sheldon refers to Penny as one of his closest friends in his good-bye video. Figuring that he would never see them again, it's heartwarming to see that at the end of the day, Sheldon really does view Penny as a close friend.
Penny and Leonard retrieving Sheldon from the comic store after their first fight. It showed that no matter how much he annoys the crap out of them, they really do care about him in the end. But that moment is really sweet.
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 Wolowitzismy 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 disastrous 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.
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.
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.
Penny: Thank you for being my friend. (hugs him)
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 apologizes, her reasoning being that she'd be devastated 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.
In episode "The Isolation Permutation" when Amy and Sheldon cuddle despite his not caring for it, because 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 and Leonard 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, and 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.
In "The Hawking Excitation", Howard blackmails Sheldon into doing humiliating tasks in exchange of getting him to meet Stephen Hawking, to get back for all the insults Sheldon gave Howard. The last task he asks is a compliment, before revealing he already talked to Hawking about meeting Sheldon.
Sheldon meeting Stephen Hawking (who actually guests stars in the show), especially because all through the episode, you see how much it meant for Sheldon.
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. This is especially heartwarming if you consider the fact that Howard's father left him as a kid.
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 Leonard's hand, which noticeably catches him off guard. But the biggest surprise is Sheldon, the poster boy for Hates Being Touched, 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? Pretty damn heart-warming!
In "The Pulled Groin Extrapolation"
Leonard: [sarcastically] You sound like you had a great night.
Sheldon: I did! How was yours?
Leonard: Not bad. I had a lot more fun with Amy than I thought I would.
Sheldon: What exactly do you mean by that?
Leonard: Well, turns out she really knows how to help a guy loosen up and have a good time. Although, truth be told, my groin is a little worse for wear.
[Sheldon hits Leonard in the shoulder with a Judo chop]
Leonard: OW! Why did you do that?
Sheldon: To send you a message. She is not for you!
Sheldon: NOT FOR YOU!
While not between the characters themselves, the bloopers for Season 5 show Simon, Johnny and Kunal talking near a makeshift panini press, but the machine malfunctions. Johnny grabs Simon and pulls him away in case something bad happens. Minor detail, but it is very nice to see the cast care for each other.
Amy asking for Sheldon to tell her something from the heart. What he tells her is something so moving and completely out of character for him. It's about how he is a mix of things around her. He then admits he got it from the first Spider-Man movie. Which is kind of sweet when one realizes that Sheldon thinks everything through thoroughly, it says something that he chose to use that particular speech, since it raises the implication that even Sheldon thinks that speech was romantic!
When Sheldon finds out Penny is unsure about her relationship with Leonard and is considering ending it, Sheldon, after many awkward scenes with the two, simply says to her "Penny, please don't hurt my friend." Penny responds that's the last thing she wants to do.
With the first couple of episodes of the season being about Penny thinking about breaking up with Leonard, "Holographic Excitation" manages to turn it around in a very sweet way. Admitting she doesn't know what he does, with some prodding by she goes to his lab to attempt to show interest into his work. After trying too hard ("What's this?" "[Technobabble science equipment]" "Oh, what's that?") Leonard slows her down and proves just how interesting and magical his work truly is, complete with a Carl Sagan-esque monologue about our place in the universe. He almost instantly becomes more attractive to Penny and she warmly smiles at him, saying "Sometimes I forget how smart you are." They even end up having sex in the lab!
"The 43 Peculiarity" had Leonard at his neurotic worst when jealous of Penny's friendship with a male British classmate. She plays it off as a funny quirk of his, but when he anonymously confronts the guy (and tries to pass off her boyfriend as being a dangerous guy with gang connections), she gets very annoyed with him. But towards the end of the episode they had this surprising conversation.
Leonard: It's hard sometimes, everywhere you go, guys are always hitting on you even when I'm standing right there. And they're always taller than me... why's everyone taller than me!? You know what, this is all in my head, this is my problem and not yours. Penny: Leonard, why do you always do this? Listen to me, you're the one I am with, you know I love you, so can you please relax because you're driving me crazy! (both freeze as they realize what she said) Leonard: ...You know, that's the first time you said you loved me... Penny: (long pause) ...yeah. Leonard: Are we just gonna pretend this isn't a big deal? Penny: That's... that's exactly what we are going to do... (tearing up) because you're about to make me cry. And we both know if I start crying, you're gonna to start crying! Leonard: (also tearing up) Yeah, you'd better go!
Howard dreads dealing with his in-laws because all his efforts to be friendly and talkative to them end up in laconic two-word responses. Upon being pushed by Bernadette to go fishing with her father, he later admits he feels the whole weekend would be futile and that they just don't mix. Mr. Rostenkowski admits he was pushed into the whole thing by his wife as well and offers to instead take Howard to an Indian Casino and teach him how to play Craps. It's especially nice because we knew Howard hadn't seen his dad since he was ten and now had something of a father figure.
Howard: Thank you, sir. Mr. Rostenkowski: (little smirk) Call me Mike.
Upon meeting Amy, Sheldon finds she is ill, and attempts to leave. Amy points out their relationship agreement states that, "In the event of sickness, the other has to look after them." Sheldon however admits that merely applies in his case and walks off. Only to stop less than a yard away, before turning and going back to her, he then admits that he did agree to help her in this case and ends with "Additionally, you're my girlfriend and I care about your well-being." one of the nicest things he's ever said, made all the more sweet by the fact he's a borderline insane when it comes his personal hygiene, and is terrified of illness.
"The Bakersfield Expedition" is close to a Downer Ending because it had the guys car get stolen with all their important things while they were dressed up in Star Trek: The Next Generation costumes. They manage to get to a local diner to call for help, all the while being mocked everywhere they go (including a slushie being thrown at Sheldon on the side of the road). Raj insisted that they still try to make Comic-con while even Sheldon is admitting defeat, in one of the saddest moments of the series. When they finally get home, haggled and exhausted, they find Amy, Bernadette and Penny getting into a heated comic book discussion after trying to find out why the guys love them so much. The lesson ended up being that while the world may not appreciate you, you can always come home to those who love and accept you.
Penny really does ruin Valentine's Day for her and Leonard. They actually talk about it and she tells him how afraid she is of commitment, even though everything in their relationship is going great. So Leonard tells her that, instead of him proposing when she may not be ready, he will wait for her to propose. After a moment of consideration, Penny asks Leonard to be her Valentine. Really hammers home how well things are going between them this time around.
Sheldon's present for Amy for Valentine's Day. Mostly because it shows how, despite making every effort not to, Sheldon actually does know Amy well enough to know what's important to her.
After years of only seeing Penny act a handful of times the final scene of "The Monster Isolation" has Leonard, Sheldon and Amy attend a class performance of A Streetcar Named Desire. What's actually nice about this scene is that while there are a few mild jokes (Sheldon excitedly waiting for the streetcars to show up) it is not meant to be comedic, Penny is doing a great job on stage and the others can't stop glowing over her performance. Even Sheldon. Sheldon did make a crack about how well she's doing on stage, yet she can't remember his orders. Still, he did compliment her work on stage, which itself is heartwarming from Sheldon of all people.
In "The Closet Reconfiguration," Sheldon accidentally reads a letter from Howard's father and is eventually convinced to tell everyone else. Howard, who never wanted to know what the note said, is hurt and upset. To make it up to him, each of his friends tell him a different thing that the note said, one of which is true. This way, he can both know and not know what the note said.
Sheldon and Leonard tell "Professor Proton"/Arthur Jefferies (played by Bob Newhart) how much the Professor's old kids' TV show on science inspired them to pursue their current science careers.
Arthur, despite all that Sheldon put him through and Arthur having a heart attack, asks Sheldon to fill in for him at a children's party. Sheldon gleefully accepts as "Professor Proton Junior."
Sheldon singing "Soft Kitty" to Arthur.
The mere fact that Sheldon didn't remark on Arthur sitting in his spot has to count.
Raj is on a date with Lucy and pressuring her to send food back to the kitchen, she panics and ends up climbing out the bathroom window. There's a problem though, the gates are locked and she has to call Raj for help. While it seems funny, Raj confesses he likes Lucy because he understands her anxiety, and they kiss. Adorableness, thy name is Kate Miccuci.
Raj unexpectedly talking to Penny without a drink in his hand, thus defying his "selective mutism" trait that had been a core of his character from the show's start. in the Season 6 finale.
The season finale has Leonard getting a job opportunity working on a project headed by Stephen Hawking. There is an initial worry that Penny might be upset about him leaving but she supports him instantly despite knowing she was going to miss him dearly and even helps Sheldon deal with his own issues. What clinches it is their parting words in the car has an "I love you" exchange, which has been a problem for them in the past.
Amy and Howard bonding over their shared love of Neil Diamond during the scavenger hunt. It's especially heartwarming for Amy, who has several early lines in the episode that ephasisize just how lonely and miserable most of her early life was, never moreso than when the hunt starts, she sees the others at the same destination, and expresses relief that this is a real game, and not some elaborate, cruel prank being played on her (these are the closest friends she's ever had, and she still feared this). She and Howard end up the only pair who had any fun that day, forgetting the scavenger hunt and karaoking Neil Diamond at the Cheesecake Factory.
Howard's song to Bernadette when she's in the hospital. Crossed with Crowning Momentof Funny. He even plans a whole special date for their anniversary, including getting their friends together.
Penny decides to do something romantic for Leonard and can't figure out what to do. She ends up showing her love by getting out the box of all the things she's saved from their relationship, which is more than enough for Leonard.
When Leonard was working with Professor Proton on his paper, Arthur didn't ask Sheldon due to him being overwhelming and annoying. Arthur finally asked Leonard why he put up with Sheldon's antics, Leonard confessed it was because they were friends. When asked why, Leonard explained that Sheldon wasn't intentional aggravating, it was just a by product of how he was, he went on to call Sheldon loyal and trustworthy and said the two had a lot of fun together, he also admitted he considered Sheldon the smartest person he had ever met and that he knew Sheldon was a bit broken and needed him, but Leonard also needed Sheldon as well. Considering how most of the time the nature of the friendship is mostly complaining brought on by Sheldon pushing Leonard to far, its really nice to hear Leonard talk about how he really feels about his friend.
Following the above explanation, Arthur decides to ask Sheldon to look over his paper as well, the look in Sheldon's eyes when he tells him this, is sweet as it clearly means a lot to him to be chosen to examine his heroes work. In the same scene Sheldon admits he already hacked Arthurs computer and thus read his paper, he however goes on to describe it as "inspiring" something which clearly means a lot to old man.
Howard and Raj's talk in the same episode, its nice to see that despite all the mocking the do really care for on another.
Watching Sheldon and Mike bonding in "The Thanksgiving Decupling" is pretty sweet considering neither of them wanted to come to Howards mothers for thanksgiving and they end up having the best time of the entire group. Plus the added fact Sheldon gets to do several father son like activities that he never got to a chance to do because his father died when he was fourteen, and Mike actually gives him the opportunity is also quite sweet.
A somewhat smaller one, but when Amy tells Sheldon he's acting inappropriately and should apologise, he manages to temporally focus himself from being drunk to get up, admit she's right and actually do so. He then actually nuzzles closer to Amy and declares she's "great". Considering how rarely he admits how he feels towards her, this defiantly counts as a heartwarming moment.