Before this, Disney had never touched modern-day New York City as the setting of an entire animated feature. (The beginning and end of The Rescuers take place there, but most of the film is set in Louisiana.) Not only did they pull it off, but then the second musical number "Why Should I Worry" starts up, and the audience realizes this is going to rock.
Upon first meeting Sykes, his dogs, Roscoe and DeSoto, go into the gang's hideout and starts terrorizing the place. DeSoto finds Oliver's hiding spot, and ignores Roscoe telling him that Sykes is calling them back, in favor of preparing to eat Oliver. Oliver responds by clawing DeSoto's nose in self-defense, leaving scars. Even Fagin says that that took a lot of guts.
When Roscoe and De Soto have Oliver cornered in their first scene and he claws De Soto's nose (which is also pretty awesome), The two pinchers, naturally, get angry and are about to kill him, when, the rest of the gang suddenly leap to his rescue! And this is the same gang that were hating him just minutes before!!! So this doubles as a Crowning Moment of Heartwarming.
Fagin coming to save Jenny and his pets, on his scooter. When you saw all through the movie how scared he was of Sykes, this definitely proves how brave he can be.
Seeing Jenny in danger, Oliver jumps into the back of Sykes limo during a frenzied car chase. He ignores the fact that Roscoe and DeSoto are in full-on attack mode and bites Sykes on the hand.
Dodger somehow saves Oliver's life after the car that they were in gets knocked off of a bridge in flames.
For Tito, driving the scooter off the railway just before they hit the train. The way he does it is pretty funny too.
Fagin, upon seeing Jenny sad and worried about Oliver, willingly gives him back to her (after pretending to mysteriously find him abandoned in a crate) despite the fact that he knows that Sykes will kill him if he couldn't get the ransom money.
Dodger and his gang ultimately redeem themselves for their friend Oliver by helping him and Fagin rescue Jenny from Sykes. Bonus points for Georgette helping as well.
Bonus points also for Dodger, who had earlier all but called Oliver a sell-out for wanting to stay with Jenny, being the one to declare that they'll save her.