Pinocchio is the name of the wooden puppet boy in the movie of the same name. He is brought to life by a fairy and told that he could become a real boy if he is brave, truthful and unselfish. Unfortunately, this proves to be difficult for Pinocchio, as he's actually a compulsive pathological liar. It's kind of his thing and, of course, his nose famously grows whenever he tells a lie - but he just can't help himself and it keeps growing and growing, even when his "conscience", Jiminy Cricket, is telling him to speak the truth.
Peter Pan is the only character on this list who has a condition that has gone on to be named after him - that condition is, of course, Peter Pan syndrome. The protagonist of his self-titled story, he's the boy who never grows up and is, therefore, very socially immature. He wants to continue enjoying the care-free pleasures of childhood, even though he's actually an adult. To Peter, time means nothing. His life, in his mind at least, is all about fun, whimsy and adventure - but this isn't always a good thing, as he can be impractical and conceited at times, which can lead to him getting himself into dangerous situations.
There's a legitimate argument that every character in Hundred Acre Wood - even Winnie-the-Pooh himself - suffers from some kind of mental disorder; Tigger has Attention Deficit Disorder and Piglet has terrible anxiety, for example. But we don't want to fill a video with them, so we'll stick to the most obvious example. Eeyore the donkey lives his life in a state of constant pessimism. He is quite literally unable to appreciate life's smallest and most basic pleasures due to his crippling depression. You only have to hear his miserable voice to appreciate how depressed the poor guy is - although he doesn't really speak that often, as his depression keeps him quiet a lot of the time.
Scar is an evil lion and the main antagonist of The Lion King movie. He is the brother of Mufasa and the uncle of Simba - and he suffers from more than one fairly serious mental condition. First and foremost, he's a complete sociopath; he killed his own brother and attempted to kill his nephew, and at the same time he also possesses that unsettling creepy charm associated with so many real-life killers. But he also has a dangerously narcissistic personality disorder, in the sense that he expects people to treat him as their superior, will stop at nothing in his aggressive quest to gain power, and doesn't care about the devastation his actions cause in the process.
The villain of the classic tale of Peter Pan, Captain Hook famously has a hook for hand, after his real hand was chopped off by Pan and fed to a crocodile. As a result, Hook suffers from post-traumatic stress disorder - a condition that is made worse by the fact that the crocodile that ate his hand constantly follows him around, after having got a taste for the pirate's blood. What heightens the condition further is the fact that the crocodile has an alarm clock in its belly, so its presence is always accompanied by a ticking sound. Is it any wonder that Hook acts how he does? His anger, his obsessive thirst for vengeance on Pan and his constant state of jumpiness is caused by a horrific event that persistently haunts him.
Elsa - one of the main characters in the hugely successful Disney movie Frozen - was born with the magical ability to produce and manipulate ice and snow. Her early inability to control her powers resulted in some terrible events - such as nearly killing her own sister. As a result, Elsa developed disorders like paranoia and agoraphobia. The paranoia rendered her terrified of using her powers for fear of causing more incidents like the one in which she injured her sister, and the agoraphobia caused her to shut herself away from society in order to ensure she didn't hurt anybody else. Of course, after ultimately learning that love was the key to controlling her powers, she got over her issues, but she certainly had them for a long time.