"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.
Leonard: You know, Sheldon really doesn't care when you pay him back. It's one of the few idiosyncrasies 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.
Small one after Penny accidentally shot a paintball gun at Sheldon's cushion and when they try to cover the evidence, Penny sits on the other side of the cushion to put a butt print. Leonard tells her the print is too small and perfect to pass as Sheldon's and she is immediately flattered.
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.
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."
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.
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.
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/Bernadette 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).
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.View.
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.
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.
A small one, but it's kinda sweet to hear Sheldon say that he actually thinks Howard is very good at his job (he kind of spoils it by saying his criticisms are because he doesn't see the value in the job itself, but the feeling is still there)
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.
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!
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!
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?" "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.
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.
"The Closure Alternative" had Penny looking for something she's passionate about, due to her friends and boyfriend having a ton of things they're crazy about (Leonard's comic books and Bernadette being able to wipe out micro-organisms with her thumb), in the end she announces to Leonard she's really truly content with her life, due to having him and their friends around. Her life is exciting already.
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.
Made better by the fact that all the options (except for Sheldon's, which was very obviously made up) were sweet, heartfelt, and showed that no matter what that note said, Howard's father did love him.
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.
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 Arthur's 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.
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.
All the more heartwarming considering how the celebrity guest stars usually react to him. Not only did James Earl Jones not get added to Sheldon's rather impressive Who's Who of restraining orders, but he invited him to come along with him on numerous fun activities, including pranking Carrie Fisher.
In "The Locomotive Manipulation," Sheldon makes a friend who loves trains just as much as him. This upsets Amy, because Sheldon ignores her and the Valentine's Day dinner she planned out. When she confronts him saying she wants romance, he says that if she wants romance, she'll get it. He then mimes and mocks all the traditional parts of a romantic encounter, but this leads to SHELDON KISSING AMY! AND HE LINGERS!
Pay attention and you can see the exact moment he goes from doing it as a joke to "wait a minute, I'm actually enjoying this". Even better is how he ask Amy to come with him to see the engine after that, instead of abandoning and ignoring her as he had been previously
Sheldon making a new friend is heartwarming in itself. He's up to eleven!
Leonard is so happy for him. "Additional data, you dog!"
In "The Friendship Turbulence", Penny, who several episodes earlier had quit her hated job at the Cheesecake Factory to pursue acting full time, has had nothing to show for it when her car breaks down and is totaled. She feels like she has no choice but to go back to the Cheesecake Factory and ask for her job back. Leonard offers to go with her to provide moral support, only to reveal he bought her a new car so she could continue to pursue acting.
After dreaming that the recently deceased Professor Proton told him to appreciate his friends more, Sheldon greets Leonard with a hug. And not an awkward, hesitant hug like he usually gives. A firm, warm embrace. No words are exchanged during the hug, and none are necessary.
In "The Gorilla Dissolution", Penny, rethinking the direction of her life, suggest she and Leonard get married. After a little banter back and forth, Leonard realizes she was completely serious and the two do make their engagement official with a ring Leonard had bought long before.
Penny and Bernadette reconciling independently, with Penny realizing that Bernie just wanted to help her, and Bernadette realizing that maybe she'd been riding Penny a little too hard. The two of them get together, and then suggest inviting Amy to go for drinks. It veers off into Funny Moment territory from there.
Leonard's speech to Penny in "The First Pitch Insufficiency" after going through several relationship tests with Sheldon and Amy (who so far scored most of them).
Penny: Let's just take the test.
Leonard: No no I don't want to.
Penny: Because you know we're gonna do bad.
Leonard: No because it doesn't matter, I don't care if we're a ten or a two.
In "The Clean Room Infiltration", Sheldon buys Amy a gift just to spite her as revenge for having to attend her Christmas party: since they had agreed not to exchange presents, Amy getting one would make her feel bad. Well, it turned out Amy did get Sheldon a present - Christmas cookies made from his beloved grandmother's recipe. Sheldon tastes one and says they're "Perfect. They taste like her hugs." It's enough to make him reconsider his feelings towards Christmas... until Raj tries to take one and Sheldon slaps his hand away.
Penny and Amy are out shopping when they were discussing how when they get together, they mostly have fun Penny's way. Penny tells Amy how she came a long way from the lonely introvert she was when they met, albeit followed with a snarky comment before stating that they can go basket weaving at a museum if that's what Amy wants
Penny: Well, you know, that was a long time ago. You're a different woman now. You're smart, you've got great friends, you've got a boyfriend, you're pretty, (Amy walks out of the dressing room cubicle in a mismatching and hideous outfit) you have zero fashion sense, but... Anyway, tonight we're gonna do whatever you want.
Sheldon finally giving the go-ahead for Leonard and Penny to move in together, beginning with one night per week. Their first night Sheldon spends sleeping on Penny's sofa.
Leonard and Sheldon have a heartfelt discussion on a lot of the things they struggle with as friends and roommates. Sheldon overtly admits that Leonard is his best friend and is fully aware of the sarcastic comments thrown his way. Both, comically, end up crying together.
Penny and Leonard putting an exhausted and over zealous Sheldon to bed, wherein they sing "Soft Kitty" to him and then comment on how adorable he looks asleep....as if he was their baby. It then turns into a CMOF when Leonard remarks on how easy it would be to smother him with a pillow.
Emily telling off the guys for playing the "Emily or Cinnamon" game with Raj, telling them that Raj has enough love for her and his dog. She promptly kisses him until she finds dog hair in her mouth...
Seeing Leonard and Sheldon work together on a project in "The Troll Manifestation", and doing so with (more or less) complete respect for each other's abilities. Leonard almost instantly runs to discuss it once he got the idea, and is compounded by Penny not only making an effort to understand his work but is very understanding when he runs out on dinner together because of his epiphany.
When Howard hears of his mother dying, Sheldon wants to say something. The others, afraid that he'll say something inappropiate, try to stop him, but Howard lets him speak. Sheldon then says the most appropiate, and heartfelt, thing he's probably ever said.
Sheldon: When I lost my own father, I didn't have any friends to help me through it. You do."
Taking it further, despite Sheldon not understanding many emotions, between the death of his father, his Pop-Pop and Professor Proton, grief and loss of a loved one is something he genuinely understands.
The toast to Mrs. Wolowitz (and by extension, to Carol Ann Susi) at the end of the episode.
Sheldon and Penny finding out in their "falling in love" game that they do love each other but more like a brother and sister (or sometimes Penny as a mother figure). Then Penny remembers fondly the day she met him and Leonard, being that it's been 8 years ago.
Albeit she should've been arrested for it, Bernadette threatening the airport employee to get the lost ashes of Mrs. Wolowitz in her and Howards' hands is this after hearing how guilty he felt about not spending enough time before she shortly died. It's nice to see despite how they bicker, she still loves him.
The cuteness of this really has to be explained fully. She opens the envelope, turns her head slightly to read the card... and her eyes widen, she gasps with a little "Oh my God! Jim Parsons!" and puts a hand to her heart, along with a huge grin. She then promptly starts squealing and bouncing up and down like a little school girl and gives him a huge hug when he comes on stage. In fact, she looks like she's more excited than Jim is.
The producers asked Newhart if they wanted his first guest appearance announced to the studio audience before filming began. He told them no, because he was worried the audience wouldn't recognize him and he didn't want to have to hear a tepid response (an understandable fear since his last major hit, Newhart ended over two decades ago). Which means the gasps of shocked recognition from the studio audience and the wild riotous applause that followed at his first appearance was completely genuine and unrehearsed. They weren't expecting him, but they knew him and loved him.
The Chuck Lorre Vanity Plate's can sometimes be dark and/or crude but the one at the end at the end of "Hesitation Ramification" bucks the trend in a nice way. The episode dealt with Penny getting a small break with a three-line bit in an episode of NCIS and she gets humiliated when her role and scene were cut out entirely. In a subplot with Raj and Stuart they were to talk with a nameless girl played by Lexie Contursi for a three line bit that also ended up getting cut for time. Lorre notes the irony and expressed regret on that part of the business, and the really nice thing is he didn't want her or her friends/family to worry that the part was cut because of the quality of her performance, the exact thing Penny was angsting over.
The Season 7 extras showed a fun experience the girls had after filming a scene where they are trying to act like adults and go to a tea party at a hotel, only to find it was mostly for little girls. Kaley, Melissa and Mayim each saw a little girl that was their "mini-me" and (with their parents permission) brought them to the main set to act as their stand-in just for fun. It's just adorable to see both the actresses having fun with the kids, but the kids are obviously enjoying themselves.