Many "Art of" Disney books contain information that wasn't mentioned in their films.
The Lion King spun off a mini-series of storybooks that revealed some of the backstory of the characters, most notably Scar's real name, Taka (unfortunately, no one told this to the guy who wrote Disney Dossiers).
Treasure Planet: A Voyage of Discovery, the art book for Treasure Planet, reveals an almost insane amount of information not included in the film, such as the name of Jim's father (Layland), Jim's relationship with him, the species and backstory of Silver, how Treasure Planet came to be, and even the names and personalities of the crewmembers.
Also, the removed songs go into great detail about a "Troll Prophecy" about Arendelle being plunged into eternal winter, going a long way to explain why Elsa's parents are so afraid of her magic and force her to hide it, as well as explaining the apprehension of everyone. Incidentally, the Prophecy winds up coming completely true anyway, just not as everyone expected.
Hans' last name, Westergaard, was only mentioned in a deleted scene from an early draft in which Elsa was still the villain. Word of God later confirmed via Twitter that, even though that scene never made it into the canon, Hans's name was kept. A Frozen Heart reveals the actual spelling of the name; previously, it had been thought to be Westerguard or Westergard as per the original asker on the Twitter post.
The Wu Sisters made it into the Kung Fu Panda video game, as did the wolves and crocodiles, though they're not so much subservient to Tai Lung as they are trying to win his favour. The game also features Tai Lung's training arena, though this may or may not be a Dream Sequence.
The two animated shorts included in the DVD releases greatly expand upon the backstories of the Furious Five and the Kung Fu Council, respectively. The latter also includes the first canonical appearance of the Wu Sisters.
The official website for Kung Fu Panda 2 gives additional info on the backstories of Lord Shen and the Kung Fu Council that wasn't brought up in the film (though the latter was Retconned by one of the aforementioned animated shorts). There's also The Art of Kung Fu Panda 2, which serves pretty much the same purpose as the first.
The DVD for Monsters, Inc. features a brief origin of monsters featurette explaining that monsters were a race of ancient hominid that came into conflict with early humans and were driven away to an enchanted island where the plant life they consumed gradually turned them into inhuman creatures of different shapes and sizes. Upon discovering this, they decided they could take revenge on the humans by scaring them and have continued ever since.
Right before the release of the 2007 TMNT movie, the writers put out a five-issue comic book mini-series that served as a prequel to the movie and basically bridged the gap between it and the previous movies.
We learn Manolo's grandmother's name, Anita, from one of Jorge Gutierrez's tweets.
Word of God states that General Posada's full name is Jeronimo Guadalupe Posada.
Chato’s name isn't stated at all in the actual movie, rather, its by the credits and novelization.
The Detention Kids’ names and ethnicities.
The fact that Xibalba and La Muerte are married is stated on the website and in other supplemental materials, but nowhere in the film itself.
The security guard that Xibalba disguises as is, his name is Guicho.
Detailed profiles of other Supers that are only briefly mentioned in The Incredibles (if at all) in the Extras section of the DVD. The comic book also fills in some holes the movie may have left open.
A fair amount of information on Titan A.E.'s world is only given in the two prequel novels.
Lampshaded (a bit more literally) in Toy Story 2, when Rex discovers the player's guide to a video game he's been trying to beat. He cries indignantly, "They make it so you can't beat the game unless you buy this book! It's extortion, is what it is." Later in the film, the tip on how to beat the game (enter the villain's lair through a secret side entrance) is used in the real world when the toys sneak into their own villain's apartment.
According to the artbook for Kubo and the Two Strings, the names of the sisters are Karasu (the chain sister) and Yukami (the pipe sister; name later reconfirmed as Washi) and that Washi's magical pipe contains a fire demon.
The Gate to the Mind's Eye is about a robot that, when the future goes to hell, travels back in time to cause a reverse Big Bang and restart the universe and let humanity go through the paces again in order to save the world. The video doesn't feature any dialogue to support this, and since it's composed of segments of animation from different producers, it is very hard to infer this just watching the video. The basics of the "plot" are only found on the VHS or DVD case.