Sheldon: Little Miss "grown-ups don't play with toys"! If I went into that apartment right now, would I not find Beanie Babies? Are you not an accumulator of Care Bears and My Little Ponies? And who is that Japanese feline frolicking on your shorts? Hello, Hello Kitty!
When Penny kisses Leonard in the Halloween episode while she's drunk, Leonard makes sure it doesn't go any further, Penny kisses him good night at his door while he's still dressed as Frodo. When Penny's ex-boyfriend Kurt sees this after him and Leonard were arguing, Leonard delivers this gem right before he shuts the door.
Leonard: That's right, you saw what you saw, that's how we roll in the Shire.
In the "Panty Piņata Polarization", Sheldon "bans" Penny from their apartment for getting "three strikes." Leonard, Raj, and Howard are too chicken to speak up for her, and the thing soon escalates into a full blown war between Sheldon and Penny, which is when this awesome exchange takes place.
Sheldon: Woman, you're playing with forces beyond your ken.
Penny: Yeah, well, your Ken can kiss my Barbie.
The resulting war leads to a few moments for both sides. And then Penny uncovers his ultimate weakness...
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?"
Remember the episode where the university student Ramona becomes obsessed with Sheldon?
Leslie Winkle(to Sheldon): Preparing your papers for the International Museum of Dumbassery?
Ramona: There won't be any room until they get rid of the permanent Leslie Winkle Exhibit.
Despite the others abandoning him, Leonard goes to convince Penny's ex to pay back the money he owes her. At first, it seems that he was only humiliated for his trouble, but later it turns out he actually succeeded.
When Leonard miscalculates some rocket fuel about to explode and tries to take it outside via elevator, Sheldon, quickly deducing that it was about to explode, walks briskly to the elevator, grabs the container out of Leonard's hands and sets it on the floor, pushes Leonard out and closes the elevator door behind him in one efficient movement. The rocket fuel destroys the elevator two seconds later.
Raj and Sheldon have a montage of "doing physics" with 'Eye of the Tiger' as the background music.
Raj buying himself a large desk for Sheldon's office.
Leonard was having a really fun time pretending to be with Penny while her dad was in town, a situation she requested because he was the only guy her dad approved of her dating. Once her dad was asleep, she snuck over to Leonard's apartment to try and chew him out, but using basic logic, Leonard managed to turn the entire conversation around.
Penny calling Sheldon out on his refusing to go to the hospital to support Howard after his mother suffers a suspected heart attack, pointing out that he constantly wears superhero t-shirts, but refuses to go to the hospital to support a friend.
The entire cast dressing up as the Justice League of America for a New Years party. It summarizes everything that makes this show awesome in one episode.
In "The Skank Reflex Hypothesis", Sheldon runs out and pulls a Heroic Sacrifice to inspire Leonard, Howard, and Raj while dramatic music plays. They actually run out and butcher the geology department, winning them the paintball trophy.
Also a Funny Moment, as Sheldon, who is more or less agnostic, pulls out a parody of the Crucified Hero Shot and after he "dies" says, "If there is ever going to be a Church of Sheldon, this is where it started".
Bernadette realizing she was in the wrong and trying to make it up to Howard.
Howard himself deserves a lot of credit for actually kicking her out of the house when she "tattled" to his mom about the issue because she had crossed the line, and freely admitted to the others they might break up over the whole thing. Coming from a guy who normally lets women walk all over him so long as they have sex with him, that showed a great deal of personal integrity.
Even his friends are suitably impressed.
Raj: Not only are you the first one of us to get married, you're also the only one of us to kick a woman out of bed. You're like a rock star!
Sheldon successfully pranking Leonard in such a awesome and hilarious way after getting pranked by Howard, Raj, and Leonard repeatedly throughout the Halloween episode.
In "The Ornithophobia Diffusion", Leonard hanging out with Penny and showing a spine by: making her pay her fair share and choosing the movie and not backing down.
Amy coerces Leonard to be her date to a wedding, which he agrees to but is clearly not enthusiastic about it. Amy actually ends up being quite a charming conversationalist and Leonard is the wet blanket cause the wedding reminds him that he "has a kinda-sorta girlfriend 9,000 miles away." Amy calls him out on it by saying "I have a kinda-sorta boyfriend who is at home playing with model trains and you don't hear me bitching about it." Surprising enough, that actually works and they have a nice time dancing the rest of the night.
Leonard finally standing up to his high school bully after letting him sleep the night at his place out of misguided good intentions.
Hawking: Are you saying I make mathematical errors?
"The Recombination Hypothesis" is about Leonard trying to figure out his feelings for Penny and whether or not they were just too different to have a future together. The entire episode is an extended Imagine Spot where he asks her out again but they start bickering and covering up their problems with sex. Just before being snapped out of his head, dream!Penny told him that he always overthinks things, and the first thing he does exiting the dream is ask her out despite the "Bad Ending" he conceived. Penny even asks if he thought this through and he replies with an exasperated nod "Yes, and I think we should go, anyways."
Relatedly, one of the ideas brought up in his daydream was that he and Penny try a "Relationship Beta Test" where they actively communicate their frustrations with each other. He later suggests the same thing to the real Penny and she is intrigued. After a rocky start with the reporting system, they actually do end up communicating better and it working almost exactly as intended.
Amy standing up to Sheldon and telling him that his behavior on date night — inviting Raj and generally being a Jerkass, is "Not okay."
Sheldon telling off Howard and Raj, who were trying to find out what Sheldon does for an unscheduled twenty minutes each day behind Sheldon's back.
He pranks them by using CGI to fake owning an interdimensional portal in a storage cupboard, pretends to be attacked by a tentacled monster, then sneaks up behind them while they're watching a CCTV recording of this on a laptop and throwing said monster puppet at them.
Made even more awesome that Sheldon correctly surmised that the two would actually believe he could pull off the "wormhole generator" he was discussing at the beginning of the episode. Basically, in order for them to believe the CGI thing, they would have to think Sheldon might actually be capable of creating a device that teleports people to other universes! That they did shows how much stock they put in his skills.
Game night that turned into a battle of the sexes, one in which the girls handily trounce the guys. Not only does Penny waste Sheldon in a wrestling match (with a Take That Kiss leaving heavy lipstick on his nose), but it also may be the only time Penny could beat Sheldon in a math-based game.
Sheldon, in "The Bakersfield Expedition", agreeing to go back home after the whole ordeal he and his friends went through. He showed remarkable self-awareness and maturity for his standards.
A little throwaway line in "The Closet Reconfiguration", but when Howard says that he's in no mood for sex that night, it really hammers home that the guy Wolowitz used to be is really gone for good.
For once, Leonard shows some spine and calls out Penny for ruining their Valentine dinner. His final joke at her expense was a great turnaround from their typical roles.
Penny: Will you be my Valentine? Leonard: ...nope! Maybe next year. (gets up to leave with Penny shocked, after a moment he turns around) I'm just kidding! Romance ninja!
Howard calling out Lucy on causing Raj to have a Heroic BSOD.
Raj finally overcoming his selective mutism, as soon as Lucy broke up with him.
In "The Contractual Obligation Implementation", Sheldon answers Leonard's challenge to spend five seconds thinking of an idea for their project, to get more women into science. Sheldon spends less than two seconds and, instead of offering an idea, points out the fundamental flaw in everything Leonard's suggested so far — all Leonard's ideas target women who are at university level and by then, it's far too late to get them into science. For once, it's nice to see Sheldon showing that yes, he really is that smart.
Leonard having fun on his own in the season premiere.
Sheldon figuring out the riddle in the comic store first, despite being the last one to arrive and read it. To make clear the scale of this, he figured out the correct answer in ten seconds flat, getting it long before every one else, even Amy. Once again, it's nice to see him showing, that yes, he really is that smart. Compounded when he reads the map coordinates for a few moments, says "got it", and then actually GETS TO USE the bowling ball he had brought along.
Amy telling off Sheldon for embarrassing her in front of her colleagues. Then, Leonard and Penny explicitly saying that Amy is right and Sheldon is wrong.
In "The Romance Resonance", Howard plans out an event to celebrate the anniversary of his and Bernadette's first date, recruiting everyone to help out with an elaborate musical number he wrote himself. When their plans went sideways because Bernadette was quarantined over a mishap at work (exposure to a raccoon virus), he didn't miss a beat and they migrated over to the hospital, with him singing to her playing a keyboard and the rest providing back-up as she watched and listened through a window. The song ends up being awesome, heartwarming, and hilarious all at the same time.
Penny gives Lucy her long overdue "The Reason You Suck" Speech, calling her out for treating Raj like shit. She even explicitly calls her "a bad person" to her face.
Regardless of how cruel he was, Sheldon's plan to teach Leonard a lesson in what its like to have OCD was awesome. He managed to manipulate his best friend into torturing himself and drove him to brink of the edge, all while barely lifting a finger. For a guy whose villainous roles are generally somewhere between a petty prankster and Egomaniac control freak, watching him play a Magnificent Bastard was awesome, and finally proved Leonard was right when he claimed he was just one "Lab Accident away from becoming a supervillain."
Leonard outsmarting Sheldon and forcing him to admit that change is good by pointing out that the only reason Sheldon has his spot, which he loves, is because Leonard bought the couch and changed the apartment. Sheldon had no come back for that.
Sheldon also gets one at the end of the same episode by managing to snatch victory from the jaws of defeat. After they've already bought the table and are sitting around it about to eat (except him and Amy, who are still in their regular places), he manages to successfully get them to all come back, simply by playing on the girls' sympathy and subtly guilt tripping them by reminiscing over happy memories that they will never have again.
Now all I need is a healthy ovum and I can grow my own Leonard Nimoy!