References to other Disney (and Pixar) movies and works:
The sneak peak features footage from Wreck-It Ralph on a big screen at the center-left. If you listen closely you can even hear some of the Japanese-dubbed lines. Some of the toys Hiro accidentally causes to fall off his shelf include a baby Cy-Bug and a Hero's Duty soldier. If one looks closely, the soldier seems to have a bit of a gut, so it might even be Ralph himself dressed up in the armor. Also, Fred has a life-sized Hero's Duty figure in his room. And apparently one of Satan/Satine as well.
Prince Hans is on a wanted poster at the police station. Next to it is one of Flynn Rider's wanted posters. Additionally, before Hiro and Baymax take off on their first flight, Baymax destroys a statue of Prince Hans.
Honey Lemon and Fred hiding in a spherical "armored" space that gets "poked" by the enemy is reminiscent of Mr. Incredible hiding in the round middle of an attacking robot, which is itself a shout-out to the Disney Short "Knight for a Day", where Goofy hides inside his oversized armor while his rival pokes at it with a spear.
Wasabi and Fred's interactions regarding how to defeat Yokai on Akuma Island is similar to the "plan of attack" scene from The Avengers, as seen here. And the way Baymax smashes through a corridor too small for him to get at Callaghan is reminiscent of a scene in The Avengers where Hulk smashes through a corridor to get at Widow.
The three comics Fred shows the others - the first villain looks like Red Skull in different colors, the "billionaire industrialist" sounds a bit like Tony Stark, and "Baron von Destruct" sounds like Baron von Strucker.
During the climax, our heroes fail to stop a black hole device that fails to shut down, built by a scientist obsessed over losing someone, just like with Dr Octopus.
The beginning of the movie where there was a remote-controlled robot fight might remind some of Real Steel. One of the robots even looks like Noisy Boy.
A very subtle one during the leaking-air scene - Baymax taping himself changes the tone, sounding a lot like the opening bars of Also Sprach Zarathustra.
The confrontation and pleading between Yokai and Krei is reminiscent of a similar showdown from The Princess Bride.
"I'll give you anything you want!" "I - want - my - daughter - BACK!"
The credits sequence includes a lot of imagery designed to invoke this, such as a suit of armor looking suspiciously like Speedy Cerviche/Yattarou.
As there is a robot protagonist, Terminator gets a shout out when things get dangerous, such as unplugging a Morality Chip causing grim determination and - for some reason - red eyes.
Baymax's actions in the climax are a reference to The Iron Giant. Both are huge robots saving their master's lives at the cost of their own. Both also live on in either a personality chip or a way of rebuilding themselves.
The montage where Baymax is built by Tadashi is exactly like the montage in RoboCop (1987) that shows RoboCop being built by a team of scientists. It's shown from Baymax's perspective and even shows Tadashi kiss him just like one of the team in the latter movie does. Baymax's armour even resembles RoboCop's a little bit.
In the credits, one can find what appears to be a half-formed "P!" symbol.
When Hiro and Baymax find Abigail in her Human Popsicle in hyperspace, Baymax clears the pod's screen for us to get a look on the sleeping beauty. This recalls a similar scene at the beginning of Aliens when they find Ripley in her escape pod. And the pod in turn is very similar to those◊ in Planet of the Apes (2001). Just add fins.