The majority of the plot hinges on one of Belle's greatest moments; willingly sacrificing her freedom forever in order to save her father.
The ballroom. Even after 20 years it can still compete with today's CGI. The fact that Belle and the Beast are perfectly animated to go along with the 3D camera certainly helps.
Belle tricking Gaston into falling out the door and into the mud.
Belle has revealed the existence of the Beast to save her father from being institutionalized, which was really Gaston's ploy to force her to marry him. She then defends the Beast, and Gaston says, "If I didn't know better, I'd think you had feelings for this monster." Her reply to a man who has the rest of her village wrapped around his finger: "He's no monster, Gaston. You are!"
During the battle at the Beast's castle, when LeFou is melting Lumiere, Cogsworth appears at the top of the stairs, dressed in British Admiralty regalia and wielding a pistol and scissors, and, laughing hysterically, slides down the banister and saves Lumiere. It's particularly awesome considering how much of a stiff jobsbody he was before, and how antagonistic his relationship with Lumiere was.
Hell, the entire castle siege in general was amazing, considering it was an angry mob of simple-minded townsfolk armed with torches and pitchforks against an entire castle of servants transformed into ordinary household objects who turn out to be Not So Harmless. You try and fight against drawers of living cutlery, a cannibal chest, and an Apron Matron teapot who utilizes her tea cup children into scalding people.
Lumiere's Moment of Awesome has to be when he saves his beloved Babette by scorching the backside off of the villain ripping her apart!
The Beast gets his when he reduces Gaston to a sniveling wretch:
Gaston: Don't hurt me, please! I'll do anything! ANYTHING! The Beast:Get Out...
The latter half of the fight between the Beast and Gaston. After seeing Belle has returned to him the Beast regains his will to live and utterly dominates Gaston, with the size and strength of a grizzly bear combined with the intelligence and agility of a human.
Actually, after the Beast stops holding back Gaston manages to hold his own, if only for a short time. Pretty impressive, considering the Beast's size and strength.
The Beast's very design is a Moment of Awesome; up until then every version had been some variation of "man with an animal's head." Disney's character is a completely new chimera who can simply be described as a "beast." He is his name.
Another moment for the design team: the way they mix his voice with animal noises. It adds an extra bit of power to his voice and emphasizes just how utterly terrifying he can be when he's angry.
The wolf sequence in the forest. Belle's attacked by a bunch of wolves; she defends herself well, but there are just too many of them. Wolf leaps, she goes down, another wolf leaps, looks like the end. Cue the Beast grabbing the wolf and ROARING in its face as the music goes berserk, then proceeding to rip the pack apart. Epic.
For that matter, the whole reason Belle is in the woods: She put reason before honor and ran away upon realizing just how terrifying the Beast can be when pissed off.
Also a Moment of Heartwarming, Belle's fear of Beast apparently disappears after he saves her. He roars right in her face when she accidentally aggravates his wounds and she doesn't even flinch. Heck, she talks back to him as he complains.
Finally, there's the moment when it becomes clear Belle has done much more than invoke a Disney Death for the Beast: the transformation sequence. This was also a Moment of Awesome for The Beast's animator, Glen Keane.
Also the transformation in the Broadway show. Absolutely breathtaking.
Gaston's rousing "Mob Song" where he paraphrases both The Bible ("If you're not with us, you're against us") and William Shakespeare ("Screw your courage to the sticking place!") to rally a, well, mob to, as the song is also known as, "Kill the Beast".
Doubles as a Funny Moment when you hear some of the other lyrics in the song.
Mob: We don't like What we don't understand In fact it scares us And this monster is mysterious at least
Here we come, we're fifty strong And fifty Frenchmen can't be wrong...
When Gaston tries to get Belle's dad into the crazy house because he tells everyone about the beast, unless Belle marries him, Belle comes to the rescue and shows everyone the beast in her magic mirror and says that he's her friend. Gaston, who sees that his plan isn't going to work anymore, wants revenge on Belle and then tells everyone that the beast is going to attack them, eat their children etc. and that they should go and kill the beast, which all men of the village are going to do afterwards. The evilness of that was extremely awesome.
The fact that this is the firsteveranimated movie to be nominated for Best Picture. Sure it didn't win, but it did what was considered to be impossible for animation at the time and establish it as a medium of story-telling and not kid fodder.
The Oscar for Best Animated Feature was added a decade later. Some have speculated that the Academy added this category specifically to prevent animated movies from having a shot at the Best Picture award.
Alan Menken's songs.
The way the choreography of the furniture's dancing during "Be Our Guest" was a Moment of Awesome.
Menken's incidental music between the songs also had its awesome moments. When Belle discovers that her father may be dying out in the cold, the Beast looks at the wilting rose and, in a moment of utter anguish, decides to let Belle go anyway, knowing it will probably doom his only chance to remove his curse. The music that plays at that moment is utter Awesome Music.
And that goes double for Howard Ashman, Menken's songwriting partner since practically the start of his musical career. Some time before The Little Mermaid won Oscars for Best Song and Best Score, Ashman was diagnosed as HIV-positive. When he was put to work for Beauty and the Beast, Ashman was noted to be irritable and would soon not even be able work in the studio. But did he give up on his work? HELL NO! He would instruct recording sessions via telephone even when he was weak and he wrote what are probably some of the most memorable songs in cinema, period, during the last year of his life (the title song's lyrics undoubtedly being his Magnum Opus). Even though he never lived to see the finished film, Ashman's sheer dedication to his work counts as this trope, a Tear Jerker, and a great Heartwarming Moment. The dedication at the end of the film states he 'gave a mermaid her voice and a beast his soul'.
Yet another out of character example: Angela Lansbury recorded the title song in a single take.
Tacked onto that is one for the person who convinced her to do it, as she hadn't wanted to perform the song and only agreed to do the one take that made it into the movie.
The message of the movie that "True Beauty is found within."
The scene where Chip fires up Maurice's wood-chopper and manages to use it to free them.
Chip: You guys have got to try this thing.
The reprise of "Belle" after she rejects Gaston's marriage proposal. The way the music swells as she runs into the field and the just the yearning in her voice, making such a simple sentiment very common among young adults very powerful and meaningful. And the way it ends on a soft, introspective note.
By the end of the third season, Vincent finally confronts Gabriel, Cathrine's killer and his son's kidnapper. Despite the shit he's done towards Vincent, he spares his life. And this is Vincent, who pretty much killed half the villains of the week for the first season (though he had a Heroic BSOD when he killed someone in the second season), so it was a pretty awesome closure to his development. Even more awesome? After he leaves, Diana is the one who kills Gabriel after he flat out tells her that he'll just get away scot free. Diana even uses Cathrine's own gun for the killing!