Baymax is essentially a robot version of Winnie-the-Pooh. Unassuming, naive, chubby, and completely friendly. (And he's an action hero!)
His purpose? Helping people and healing. His friendliness and chubby-cuddly aesthetic are all because of that, so that he won't scare kids, the elderly or stressed people.
When Yokai is pursuing Hiro and Baymax in the warehouse, and the latter is moving slowly (not on purpose), Hiro runs back and grabs Baymax's hand. After turning a corner, Hiro immediately pushes Baymax in front of him. This moment is especially sweet because Hiro could have left Baymax there, since he's a robot.
Baymax comforting Hiro after he injured his foot, and going a bit overboard.
Baymax: (picks Hiro up and cradles him like a baby) It is alright to cry. Crying is a natural response to pain.
"You will be alright. There, there." (pats Hiro on the head)
Big fluffy kitty + big inflatable robot = adorable.
The scene where Baymax huddles over Hiro and turns on his heater, followed by the rest of the team lying on him.
When Hiro apologizes for his dangerous behavior, GoGo shuts him up by hugging him.
GoGo: We're going to catch Callaghan, and this time, we'll do it right.
What makes this more heartwarming is that she was the first of the group to forgive Hiro, said hug could have been given by the more openly affectionate Honey, but instead it's GoGo that does this to show to Hiro the depths of her sister-like care towards him that lie underneath her cold exterior.
If you pay close attention, you'll notice that the gang isn't really mad at Hiro for what he did on the island. Sure, they didn't agree with his actions, but no one yelled at him over trying to use Baymax to kill Callaghan. They just tried to calm him down and talk some sense into him. They know that Hiro isn't the one to blame for that. Callaghan is.
Honey is a walking Moment of Heartwarming with her cute voice and fun personality. Looking at her just makes you want to go "Awwww!". She's like a humanized Uni-Kitty, but without the anger face!
The fist bumps between Hiro and Tadashi.
By extension, the fist bumps between Hiro and Baymax.
Baymax's fist bump sound. TOO. CUTE.
The reel of Tadashi trying to create Baymax. During the first trial run, Tadashi is chipper and excited. Unfortunately, he receives failure after failure, some downright painful. By the eighty-fourth test, hes exhausted, jaded, and likely one more explosion away from throwing in the towel. Then he finally gets Baymax to work.
Tadashi: It works. IT WORKS! Oh, this is amazing, you...you work!
Tadashi: Oh man, wait til my brother sees you. You're gonna help so many people, buddy, so many. That's all for now. I am satisfied with my care.
"I'm not giving up on you. You don't understand this yet, but people need you."
"Wait 'til my brother sees you"... Tadashi has just made the biggest breakthrough of his life, and all he wants to do is share it with his little brother.
Which is all after Baymax points to his chest and says "Tadashi is here" before cuing up the video.
Even more touching is that during the above quote, Tadashi is looking straight into Baymax's camera — and effectively at the audience. This could mean the world for any viewers who need some uplifting words.
Combined with the above point, in-universe Hiro is looking right at Tadashi as the recording says this. Baymax knows it's exactly what Hiro needs to hear at the moment.
Here is the most important part of that scene, recreated in gifs.
During the credits, the officer at the station is shown with a new tape dispenser as a gift from Hiro and Baymax, and the officer is smiling.
The credits also show a news article about the opening of a new building at the college, named after Tadashi.
Looking closely, you can see that Alistair Krei is the one who's unveiling the Tadashi Hamada Convention Hall. It's a nice touch to show that, really, he's a pretty good guy.
This exchange between Hiro and Krei before the former goes into the portal to save Abigail.
Krei: The portal is destabilizing; you'll never make it! Hiro: She's alive in there. Someone has to help.
Honey gives Hiro cheek kisses in her introductory scene.
After Tadashi's death, Hiro spends weeks holed up in his room. At one point he receives a video-message from the others, recorded on Honey's phone, saying they miss and are here for him. Probably the best part is the last line, from Fred of all people.
Fred: Hiro, if I could have only one superpower right now, it'd be the ability to crawl through this camera, and give you a big hug.
It makes even more sense if you read some of the supplementary material. Fred is involved in many not-for-profit volunteer organizations, so much so that he was written a recommendation to be the mascot of someone else's school. One of those organizations is an expy of Big Brothers Big Sisters. Fred belonging to such an organization is a CMOH in and of itself.
A major source of conflict between the brothers during the first act is Hiro using his incredible skills in robotics to hustle and win at illegal bot fights. Tadashi claims he could do much better, and Hiro retorts something to the effect of "What, and go to a boring old college like you?" Tadashi then proceeds to show him just how "boring" his college is and what Hiro could really accomplish if he applied.
When Tadashi first rescues Hiro from the angry bot-fighters, he asks if Hiro is okay before he starts scolding him.
Cass does the exact same thing when she picks the pair up from the jail. Tadashi comes by it honestly.
The fact that four young adults were so accepting of their best friend's kid brother that they stuck it out with him all the way to the end, doing whatever they could for him; they may just be the best friends he's ever had.
Note that on the montage of Hiro creating the Microbots, you see the occasional frames of the gang helping. In the limited time of the film, it was a good way to show their bond forming even before the main plot kicks off.
On the other side they are a big reason Hiro wants to get into their school.
Not to mention that they were all extremely close to Tadashi. Their desire to stick with Hiro may also be fueled for their love for him.
GoGo: Tadashi Hamada was our best friend. We're in.
When experimenting with his flight for the first time, Baymax notes an increase in Hiro's brain activity. When Hiro asks what that means, Baymax says, with surprising emotion "The treatment is working!" Which leads to a first flight even Tony would have been jealous of.
Baymax: I fail to see how flying makes me a better healthcare companion.
Hiro: I fail to see how YOU fail to see THAT IT'S AWESOME!!! FULL THRUST!
While resting on a wind power turbine after their first flight, Baymax notices Hiro's feet swaying, then proceeds to copy him.
Hiro's demonstration of the Microbots is this, because it felt like a tribute to ol' Walt himself, kinda like a subtler version of the "keep moving forward" Arc Words from Meet the Robinsons. The whole thing was so very much like the "brighter tomorrow" shows, displays, and tech demos that are liberally incorporated throughout both Tomorrowland and Epcot Center.
Or the Stark Expo.
At the end of the presentation, when everyone is applauding Hiro, Cass is manically shouting "That's my nephew! My family! I love my family!" While tugging the arm of the stranger next to her, who just smiles at this.
At the end, when Hiro fist-bumps the gauntlet Baymax rocket-punched to save him and Callaghan's daughter, the fist opens to reveal Baymax's personality chip. Then we see Baymax wake up to see Hiro again and they hug. Revealing that Hiro had rebuilt him exactly how Tadashi designed him.
To boot, the shot is set up just like the video of Tadashi - from Baymax's perspective. It goes to show how Hiro has become more like his brother. He's even in Tadashi's old office.
It's even cuter, because Hiro makes the same noise that Baymax did when giving someone a fistbump. It's just as cute as when Baymax does it.
The moment at the end, though this is probably up for debate: Baymax had his memory chip closed in his fist when he fired the pod with Hiro on it back through the portal. Since he had taken the chip out before he sent them back, it could be read that trying to save Hiro was something he was doing of his own free will - he no longer had the chip inside to compel him to protect humans.
It's not a specific moment, but it deserves mention: the relationship between Hiro and Tadashi, everything that entails. In particular if you have a brother, young or old, whom you feel is wasting his potential, this will get to you. It may not quite be what Frozen did for sisterly relationships, but it comes very close.
Just the idea of Baymax: Tadashi built a robot. Not as a weapon, or as a soldier, or even as some sort of mindless servant. Instead, he built a robot designed to care for people and is physically incapable of harming others, even on accident (due to Baymax's inflatable, and incredibly soft, composition). And also manages to be so incredibly non-threatening in appearance that he can't even scare people on accident (Which is important for someone who may be helping the elderly or those with a weak heart). Tadashi succeeded in building a robot that is perfectly designed for its purpose... for no other reason than to help people.
Indeed, he build Baymax so well that even Baymax realizes how important his appearance is, among other things.
Baymax is generally implied to not have true AI... yet still becomes increasingly resistant to Hiro making him into a weapon out of what certainly seems to be sincere respect for Tadashi's original vision. Further heartwarming comes from the fact that this might well have stopped Hiro from becoming a villain in his darkest moment.
Callaghan learns that his daughter is alive near the end of the movie. It becomes a Tear Jerker when he realizes he probably won't see her for a long, long time.
When Baymax is returned from a killing machine back to his original state, the first thing he does is apologize to everyone for any harm he may have done and express regret at violating his health code. Sure, it's his programming because he's designed to be kind-hearted and caring, but it still counts.
If you look closely, Heathcliff gives her a brief smile—one of the rare times his Comically Serious exterior cracks.
and does it again with Wasabi
Fred greeting Heathcliff by calling him "my man" and both giving each other fist-bumps.
Fred after lamenting the distance between him and his busy father, discovers his father's secret superhero lair. The man himself walks in and reveals that they're not so different in more ways than one, reciting Fred's gross underwear rhyme - and you can hear the joy and pride in every word. And then they happily hug each other.
While Hiro made upgrades and gave everyone else new abilities, he didn't make anything for himself except a suit. This could be either because he trusts Baymax to protect and fight for him or that there wasn't enough time to upgrade both of them and he decided to devote his time on Baymax.
Not a specific moment, but compare Baymax's first hug for Hiro to the last two times he hugs him. The first time, his eyes are wide open and staring ahead. The last times, both before sending Hiro and Abigail out of the void and when he's rebuilt and reunited with Hiro, his eyes close. Just like a human being does when they are fully, emotionally-invested in the hug. It's subtle, but still heartwarming and a great sign of his Character Development.
Tadashi helping Hiro by grabbing his ankles and flinging him around, so he can "look at a different angle". It works. Plus, it's also a cute moment of sibling love.
Look even closer, Hiro is letting his body dangle. What does this mean? He trusts that Tadashi won't let him fall.
Hiro and Tadashi's relationship with their Aunt Cass. She took them in, even though she never had any experience with raising kids. And even though it's not shown in a lot, Cass is a kind, motherly, and eternally supportive figure in the lives of her nephews.
The picture on the page of Hiro hugging Baymax after successfully rebuilding him.The entire hug is adorable, especially the way Hiro snuggles his head into Baymax's chest.
When Hiro and Baymax go to save Abigail from the hyperspace Baymax says that flying makes him a better healthcare companion. Initially Hiro upgraded Baymax so he could get answers and revenge on Yokai. He violated the purpose behind Baymax by turning him into a war bot. But at the end of the movie Baymax himself acknowledges that, in a roundabout way, Hiro furthered his brother's ideals.
The fact that Fred never gave Tadashi a nickname might imply that the two of them aren't close, except that their interactions prove otherwise. This implies that, rather than it being a lack of closeness, it's due to the respect that Fred feels towards Tadashi: Tadashi is or was the unofficial leader of the group at the science club, and of all of the group, Tadashi was the one who got along best with Fred, from what we get to see (He even compliments Fred on his Underwear Recycling method). As such, the lack of a nickname is a sign of the utmost respect. It would be the equivalent of Fred calling someone "sir", and meaning it. Fred even wears formal attire at Tadashi's funeral, and seems to have taken Tadashi's loss as bad as Hiro did.
At the beginning of his demonstration of the Microbots, Hiro initially gets stage fright and stumbles over his introduction - not helped by his microphone loudly feeding back and one guy looking bored and walking away. Tadashi, who is in the audience, notices this and quietly tells him to breathe. Hiro does so, and this calms him down enough to get on with it, and his confidence builds up the further he goes on, resulting in an epic Moment of Awesome of a demonstration.
And if you look closely at GoGo's face, she sends a glare towards the man who left. Aaawww.
Before Hiro demonstrated his microbots, everyone was reassuring that everything would be fine. Honey told him his microbots were amazing, GoGo told him to "woman up", and Wasabi offered to give him deodorant, breath mint, or a fresh pair of underpants to ease his nerves.
Considering the response to the movie, the fact that soft robots are an actual field of research, and that Disney has created at least a semi-mobile version of Baymax, it's not entirely impossible to think that such healthcare robots with a Baymax type aesthetic may exist sometime in the near future. Tadashi would be proud.
Not to mention that as of January 2015, the Innoventions attraction in Epcot has been rumored to get a Retool themed around this movie. This goes very well with both projects' promise to inspire kids to do great things.
One Tumblr user by the name of untranslatablerecreation posted some deleted storyboards, many of which demonstrate Hiro and Tadashi's strong brotherly love.
One for Disney. Many people have accused the company of lacking cultural sensitivity, rightly or wrongly. This movie takes a comic book that the Japanese despise for being horrifically stereotypical and insulting their culture and transformed it into a movie that the Japanese adore, both for the much more tasteful use of Japanese culture and the diversified cast.
Related, but the reason the city is called San Fransokyo and is such a mixture of Japanese and American culture? Because after the San Francisco earthquake of 1906, Japanese immigrants helped rebuild large parts of it.
Hiro didn't know that Baymax was active or even operational. But he still kept him in Tadashi's room, which doesn't look like it's been touched, with his hat even on the bed. Baymax is both a piece of his brother and also Hiro's chance to be the older "brother" to him.
For the Chinese Zootopia campaign Byron Howard made this poster◊ as part of the campaign for the movie in China which shows Baymax holding Judy and Nick.