Especially when Woody spreads his arms and shouts Buzz's catchphrase
Woody's plan to save Buzz and help all of Sid's toys.
"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... 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.
Heck, Toy Story in itself is a Moment Of Awesome. 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 wit and heart.
Buzz saving Woody from Scud. Especially counts after Woody hopelessly saying "Take care of Andy for me!" while being dragged out of the moving truck.
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.