Heartwarming / Captain America: The Winter Soldier
Natasha wanting to fix Steve up with someone throughout the movie.
And finally, before leaving to form a new identity for herself after all the events that transpired and even giving him a rare dossier on The Winter Soldier project, all she truly asks of Steve... is to ask Sharon out on a date.
Steve and Sam recognizing each other as veterans and connecting after their run. Steve might be a Fish Out of Temporal Water, but there are still people who have shared the experience of going to war and coming home and trying to adjust.
Not to mention Sam standing vigil at Steve's hospital bed.
Plus the fact that he takes in Steve and Natasha even after being told everyone is trying to kill them. He's only known Steve a few days, but he trusts him completely and is willing to go to bat for him.
When Sam offers to help, Steve assures him that he doesn't have to, noting that he left for a good reason. Sam responds that Captain America needs his help, and that's as good a reason as any to get back in.
Sam worrying about Steve after he finds out the Winter Soldier is his former best friend, and going with Steve to look for him at the end even though he tried to talk Steve out of thinking of him as Bucky.
When Steve sees the picture of Sam's pararescue unit, and quietly asks, "Is that Reilly?" Even though they're in the middle of putting together a mission plan, Steve remembers and respects Sam's loss.
Steve's flashback to Bucky comforting him after his mother's funeral after learning that his best friend is the Winter Soldier.
Steve: Even when I had nothing — I had Bucky.
The entirety of Steve and Natasha's friendship throughout the film.
In the beginning they're basically friendly co-workers who have different philosophies about their job. Their friendship deepens as they begin to trust and get to know each other more while they're on the run.
Steve's friendships with Natasha and Sam in general, along with that little notebook filled with the pop culture he needs to catch up on. It shows that he's accepted his situation, that there's nothing that can be done to change it, and that he's able to do what everyone from his past would want him to do: move on and live.
Steve saying, with complete sincerity that he trusts Natasha. After a life time of being a spy and assassin, after finding out that SHIELD was not on the straight and narrow, the world's biggest boy scout is telling her he trusts her absolutely.
The stunned look on Nat's face doubles the heartwarming. Steve managed to break through her snarky trust-no-one persona and make a friend.
Bucky saving Steve's life after he falls from the helicarrier. And Steve's decision to look for him. And Sam's decision to follow Steve no matter what.
After Maria Hill rescues Cap, Black Widow and Falcon, they express the need to get Natasha medical attention, to which Maria replies that she has to see Fury's alive first.
A small bit of Fridge Heartwarming: When Fury talks to Steve and Nat after, he says he didn't tell them at first because he didn't know who he could trust. Maria was already there, suggesting that he knew he could trust her - even after what went down during the deleted scenes of The Avengers. These two are co-workers and allies, but more importantly, they're friends who trust one another.
When Steve orders Maria to make the three carriers shoot down each other, she hesitates, knowing that he's still inside one of them. It's never indicated how close they were in previous interactions, but it's telling that Maria tries to protest his self-destructive order by brokenly calling him "Steve" instead of "Captain Rogers".
The fact that there actually seems to be a legitimate friendship of sorts between Natasha and Fury is pretty heartwarming in and of itself. Note Fury dropping his gun when Nat's life is threatened, and the quiet, urgent way he says her first name when she knocks herself out to short circuit the explosive that was endangering her.
The Captain America exhibit at the Smithsonian really hits home the impact that he had on history. Bearing in mind that this exhibit is probably from BEFORE he was found in the ice, and will have become even more prominent after the events of The Avengers, too. And you see that his uniform (that he crashed the Valkyrie in) was recovered and is on display along with the rest of the Howling Commandos' uniforms.
The mere fact that the exhibit isn't just all about the Cap - Bucky and the Howling Commandos have their own displays and are acknowledged as heroes, too.
When Steve visits the place incognito, one little boy, wearing a t-shirt bearing Cap's trademark shield, recognizes him and silently stares in shock. Steve's reaction to this? He smiles gently and raises his finger to his lips in a "shhh" motion; the boy nods in understanding and remains quiet. It's small but adorable.
Steve visiting a theater which was showing an interview of Peggy from 1953. She talked about how he rescued over a thousand men from a HYDRA camp, including the man who would eventually become her husband. The fact that she also stated that even after he died Steve was still changing her life shows that she never stopped caring about him.
Natasha wears a tiny arrow charm on a necklace (which is actually a real necklace from Tiffany & Co.) for much of the movie. It seems an obvious tribute to Hawkeye. Whether one is a Black Widow/Hawkeye shipper or not, it's pretty damn sweet.
When Steve has a flashback to happier times with Bucky after learning the identity of the Winter Solider, it's shown that both Bucky and his parents clearly cared a lot about Steve (Bucky says that his parents wanted to give Steve a lift to his mother's funeral). Bucky even offers to have Steve move in with him, with his comment about Steve "just having to shine his shoes" indicating he'd be willing to provide for both of them.
It even subtly shows a similar dynamic from the first movie: unlike everyone else that looked at Steve, Bucky has never seen him as anything less than an equal in all regards.
Steve: I can look after myself.
Bucky: But that's the thing, you don't have to.
Steve refusing to fight his old buddy and especially when he quotes him in the final line both tears up the eyes and warms the heart:
Steve: I'm not going to fight you.[drops shield out of the Helicarrier] You're my friend.
Bucky: You're my mission. [savagely beating him, punctuating each word with a punch] YOU'RE! MY! MISSION!
Steve: Then finish it, 'cause I'm with you to the end of the line.
At that moment, this almost crosses into a freakin' fridge moment of awesome, heartwarming, and a tearjerker all at once— Bucky is prepared to finish the job, but when Steve drops the final line from the above entry, The Winter Soldier's expression completely changes— it goes from this◊ to this◊. You could say that the first image is The Winter Soldier, and the second is Bucky Barnes.
Also, given the fact that The Winter Soldier is essentially a computer in a human's body whose memories have been deleted, Steve pretty much broke into a supercomputer and recovered Bucky's memories from the Recycle Bin just by taking a beating and knowing the right things to say (and wear). That'd be akin to un-deleting a file, which someone else axed, using only your mind.
It's hidden inside a moment of horror but the Helicarrier's targeting system showed Tony Stark finally returned to New York after his anxiety attacks in Iron Man 3.
The Winter Soldier traveling to the Captain America exhibit in the Smithsonian in The Stinger. It shows that he really does want to remember who he was.
The way the Winter Soldier's brainwashing begins to break down every time he sees Steve, even right after a memory wipe. He even seems to begin to remember him during their first encounter, before Steve recognizes him.
When Captain America gets on the PA at the Triskelion after being chased by SHIELD for half the movie to explain his side of the story (Without any evidence to back up his claims whatsoever), nobody even considers the possibility that this is a criminal who is lying to justify his crimes or to confuse people who could potentially stop whatever he's up to. Every member of SHIELD who isn't in on the conspiracy turns on their HYDRA coworkers to try to stop Insight. This shows exactly how respected the Captain is, even after seventy years.
Special mention should go to the man at the computer who refuses to launch Project Insight. It's one thing to stand up for something and have a weapon with you. It's another thing entirely to be completely defenseless and yet never back down even with a gun aimed at your head.
Computer Tech: Sorry, sir. I'm not going to launch those ships. Captain's orders. Rumlow:[draws gun] Move away from your station! Agent 13:[as she and everyone else draws their guns] Like he said: Captain's orders.
Plus the Quinjet pilots who readied themselves because "We're the only air support Captain Rogers has got!". Pity the Winter Soldier killed them all so spectacularly.
A subtle one goes to the World Security Council members. In The Avengers they had referred to Captain America as a freak and had been willing to nuke Steve and the rest of the Avengers. However, they also immediately believe his claims about Hydra's infiltration without any proof whatsoever. That's good enough, but after Black Widow starts dumping SHIELD and Hydra's top secret files onto the internet none of the Councilmen object. They fully trust all of the Avengers now, enough to implicitly agree to destroy an organization they lead.
Steve's Imagine Spot of his pre-serum self lagging behind the rest of his platoon during a running drill, and giving a stunned look to the man he would become.
This one is a meta one for Robert Redford. When Pierce is in his home and he opens up the refrigerator, you can briefly see a jar of Newman's Own Spaghetti Sauce on one of the shelves. Awwww, best friends together on screen again!
Sam sitting by Steve's bedside with "Trouble Man" by Marvin Gaye playing, and there is one last "On your left" muttered by Steve.
Think about this: if Steve is on Sam's left, Sam is on Steve's right. Sam is Steve's right-hand man.
A small one, but a meta one spanning both this and First Avenger; Steve promised Dr Erskine that he would remain not a good soldier, but a good man. Even after 70 years, Steve has kept that promise by caring for the freedom of others, and not blindly following orders.