Beforehand, when Woody and Buzz are launched up into the sky.
Woody: This is the part where we blow up!
Buzz: Not today!
Woody's plan to save Buzz and help all of Sid's toys.
Woody:(through his speaker) From now on, you must take good care of your toys. Because if you don't, we'll find out, Sid. We toys can see everything...
(He then proceeds to break the masquerade and comes to life in Sid's hands).
Woody: So play nice.
This also counts as Nightmare Fuel due to the manner in which the toys scare the sadistic Sid straight.
Using perfectly executed teamwork to get Sid's dog locked out of the house.
Buzz saving Woody from Scud. Especially counts after Woody hopelessly telling him to take care of Andy while being dragged away from the moving truck.
Woody:[after Scud grabs his leg] I can't do it. [begins to slip] Take care of Andy for me! Buzz:[jumps at Scud]NO!!![grabs Scud's eyelids to make him let go of Woody]
Shortly afterwards, Slinky attempting to pull Woody and Buzz up, at great risk to himself.
Buzz "proving" he can fly during his introductory scene. Yeah, we all know it was due to (unknowingly) hanging off a ceiling mobile, but it's still pretty damn cool.
When Hannah finds out Sid now fears toys she takes her revenge.
Hannah: What's wrong Sid, don't you wanna play with Sally?
The original script unfortunately had such an unlikeable domineering Woody that when the other toys finally turn on him for (this time intentionally) throwing Buzz out of Andy's room, it is nothing short of cathartic. The punchline truly comes from Slinky, who at this point was a downtrodden right hand dog that Woody was trying to bully into keeping the others in line.
While not as dramatic as the climax of the finished film, the early storyboards had a pretty awesome way for dealing with Sid - just as Sid prepares to light the rocket, Woody casually comes to life, strolls up to Buzz and unties him. All while questioning what deep-seated issues would cause a child to act like him. Buzz, initially baffled by Woody's actions, soon joins in, and the two end up having an intelligent debate over Sid's psychological problems, all while poor Sid is reduced to a gibbering mess at seeing two toys come to life and psychoanalyze him.
The movie itself. Keep in mind what CGI was to the moviemaking industry in the 1990s. Jurassic Park only came out two years prior, and CGI was firmly in the action movie genre's grasp. It wasn't a kid's movie thing, it was a workaround to make scenes that would normally be impractical, impossible, or just too expensive to accomplish with practical effects alone. People simply didn't think CGI could be a cartoon, or that it would be so good at it. It revolutionized animation and cinema, put Pixar on the path to becoming a household name and a cinematic Seal of Approval—and it did so with basically just wit and heart.
The cherry on top is how well Toy Story has aged. Time has definitely worn on it, but take into account CGI's notoriously short shelf life, and the fact that it's still watchable at all is impressive.