Toy Story 3 doubles as an example of Darker And Edgier within a series, and was an especially memorable case, since it took a series with a reputation for lightheartedness and gave it a Prison Episode.
The Incredibles: With gun violence, Electric Torture, suicide attempts, large-scale destruction, bad guys who Would Hurt a Child, and "good guys" who run from the police and lie to their own families, all in the same film, The Incredibles may very well be the darkest Pixar movie yet. Brad Bird's history of working on The Simpsons really comes through here.
Brad: "Really, really little kids should not see this movie. They should wait till they get older. We're getting some reactions from people who were disappointed that their four-year-old was a little freaked out by it. Well, I don't want to compromise the intensity in order to please a four-year-old."
Frozen is a major, major contender for this, despite having a bodycount of only 2 minor characters (the King and Queen), and the villains punished justly without death. The film features childhood trauma, dead parents, murderous noblemen, a comic relief character that spends the movie dreaming about what would kill him, and the entire cast nearly dying in a massive snowstorm near the end.
Not to mention the whole plot of the movie is about childhood trauma.
Even in comparison to the first movie, the sequel is perhaps even darker. Its Villain Song is considered much more intense than that of the first, subjects like child abuse and war are dealt with much more bluntly, and the violence is both heavier and more frequent.
Disney's Pinocchio. That thing was dark both literally and metaphorically. There's a few really horrifying sequences such as the scene where a boy is seen turning into a donkey, made even worse when we see tons of other boys being turned into donkeys who are either sold to the salt mines or kept to pull the carriage to take more boys to the island to meet the same horrifying fate. Even more unusual for a Disney film, there are three different people who serve as villains (four if you count Monstro), and all of them get away with the things they do, including the ruthless coachmen who kidnaps boys and turns them into donkeys.
Mulan thoroughly addresses the subject of war, and the grim consequences thereof, including the implied large-scale murder of the innocent and the grieving family members of those killed. Unfortunately, it is ruined by the inescapable comic relief that plagues it.
And Mulan's strategic avalanche-triggering makes her personally responsible for the deaths of hundreds of men, something you cannot say about any other Disney Princess.
How to Train Your Dragon wasn't that dark or edgy, but it was more serious compared to most of DreamWorks' other animated films, and it's certainly Darker And Edgier than the book it was based on.
The sequel takes it further. Here, the Big Bad wants to enslave all dragons, there is a battle with a gigantic ice dragon and one of the main characters dies.
The 2009 made-for-DVD animated film Wonder Woman takes this approach. Wonder Woman is shown killing on numerous occasions, including cold-bloodedly killing several guards (including two who have their throats cut by her tiara). The film also ramps up the sexual innuendo.
Kung Fu Panda 2 is significantly darker than the first film. Multiple characters are Killed Off for Real on screen, (though we don't see their bodies) and the Never Say "Die" rule is broken a LOT, to the point where it seems like "death", "dead", and "kill" are used every other sentence. The villain wants to take over all of China with giant cannons that are seemingly unstoppable and really are used to kill. And then there's the repressed memories of Po's traumatizing childhood, which involved the attempted genocide of his entire species.
The first film was also an example in comparison to most other DreamWorks Animation films at the time, which were mostly pure comedy while Kung Fu Panda is an action/comedy with some pretty serious drama thrown in as well. Even the comedy is a bit more mature, with Dreamworks dropping the pop-culture jokes that they had been previously known for. This is a trend that would later be continued by How to Train Your Dragon.
Transformers: The Movie compared to most of the rest of the series, the original series occasionally took a darker turn but everything usually turned out fine in the end, but in the movie the vast majority of the original Autobots are killed within the first 20 minutes in increasingly gruesome manners Optimus Prime included, later the surviving Autobots (mostly newer characters) band together to save the world from Unicron, a planet eating Transformer, while having to avoid Galvatron, the rebuilt Megatron.
Digimon X-Evolution. When Digimon die, they actually leave their corpses behind, the hero has an attack called "All Delete", and previous heroes are ruthless killers.
Epic is this to Blue Sky Studios' otherfilms. As Blue Sky stuck mainly with comedies, this is their first film where the action is pushed to the forefront. Characters die, and a few have major daddy issues.
With an ending thats pretty bittersweet.
Despicable Me: In the first film, when the girls were taken by Vector, things just got really serious. Especially the sequel, Never Say "Die" is averted multiple times, and the villain's plans for global domination are to set the Brainwashed and Crazy minions (who are turned into omnicidal maniacs as a result of the PX-41 serum) onto the major continents if world's leaders don't hand over control to him. And he wants Gru to help him.
The Secret of NIMH is much more frightening than than the novel Mrs. Frisby and the Rats of NIMH. While it has does have some elements of Disneyfication, the majority of the events are Played for Drama more than in the book, considering the protagonist is a mouse. For example, Brutus scares off Mrs. Brisby with a spear rather than simply turning her back from the rosebush. Then there's onscreen blood, an evil villain, multiple violent deaths, and the threat of Mrs. Brisby's home sinking into the mud, all of which were completely absent from the novel. The director and producers tried to get a PG rating to appeal to a wider audience, but it rated G anyway.