Andy's Mom refusing to sell Woody to Al at the yard sale despite him giving her some pretty high offers for a children's toy. Mom not only turns him down but is smart enough to lock Woody in a box so that someone won't come along and steal her son's favorite toy. It doesn't work, but points for trying.
"Woody's Finest Hour" escaping from the plane.
The true crowning moment comes from Bullseye, who managed to keep pace with a jet liner.
Buzz talking some sense into Woody, reversing their roles in the first movie.
Buzz: Woody, stop this nonsense, and let's go.
Woody: Ah, Buzz. (sighs) I can't go. I can't abandon these guys. They need me to get into this museum. Without me, they'll go back into storage, maybe forever.
Woody's rescue of Wheezy (done with only one working arm no less).
The fact he does so using Buster, and even has him obey his every command perfectly, despite it being implied the human owners have failed to remotely train him.
Buzz figuring out the thief's identity from two minimal clues: a Vanity License Plate reading "LZTYBRN" and a bunch of feathers that fell from his car trunk.
The toys tracking where to find Woody at Al's Toy Barn: Hamm scans the TV channels at breakneck speed to find Al's commercial, and Etch stands at the ready to quick-draw a map when Al announces the address.
Buzz and co. blinding Stinky Pete with cameras to save Woody, then proceding to dump ol' Pete in the backpack of an "artist".
Woody: Happy trails, Prospector.
The battle between the other Buzz and Zurg. To the audience and the other toys, they look like idiots. To the two of them, it's a battle between a Space Ranger and his Arch-EnemyThe Emperor, with laser shots and ion blasts filling the air.
The moment when Zurg makes his entrance, rising into view of the group on the roof of the elevator car, the light from the hatch illuminating him from behind, and declares "So, we meet again, Buzz Lightear — for the last time!" Palpatine himself would be proud of such an introduction.
This one is subtle: Other Buzz works his way rung-by-rung up the elevator shaft, so to speak, dragging the other toys below him. He visibly struggles with each inch when he see him later, then we see he'd gotten about halfway between the 22nd and 23rd floor. Let's go over that again... he'd scaled the elevator shaft, from the ground floor, to at least the 10th story. And this was while burdened with the other toys' weight. That deserves some props for that level of strength and endurance.
Buzz reuniting with the group and proving beyond a shadow of a doubt he's the Buzz they all know and love by silently lifting the other Buzz's helmet up causing him to gasp for air (just like Buzz himself did in the first one) and then lifting up his foot with Andy's name on it.
That scene. You know the one. The one with the old man (Geri from the Pixar short, "Geri's Game") fixing Woody. His old, shaking hands and his clear near-sightedness makes the audience nervous at first, but the instant he actually begins his work, we see that he has an incredibly skilled, practiced, and gentle hand, causing all worries to rapidly fade away.
The opening sequence with the Buzz Lightyear video game. Rex has some mad gaming skills besides his stubby arms.
In video game adaptation of Toy Story 3, you actually get the chance to play that fictional video game! Awesome, isn't it?
Buzz: Did Woody give up when Sid had me strapped to a rocket?
Buzz: And did he give up when you threw him out of the back of that moving van?
Potato Head: Oh, you had to bring that up.
Buzz: (as the Star Spangled Banner begins to swell and appear behind him) No, he didn't! We have a friend in need, and we will not rest until he's safe in Andy's room! Now let's move out!
We have the toys working together to drive a car by stealing a Pizza Planet truck, to be precise to get to the airport in time.
Mr. Potato Head grabbing the 3 little aliens JUST as they were about to fly out of the Pizza Planet truck. No wonder they kept pestering him about how they were eternally grateful.
This becomes even more awesome in hindsight, as by saving the LGM, Mr. Potato Head indirectly helped save everyone from the incinerator in Toy Story 3.
Also from Mr. Potato Head, his Oddjob moment where he quickly flings his hat perfectly between the front doors of the building to stop them closing.
Galyn Sussman backing up the entire film on her home computer before the film was accidentally deleted and the emergency backups failed.
In spite of several months of serious Executive Meddling, Pixar managed to rewrite then complete the film in less than a year, persuading their executives to release it in cinemas again. This allowed them greater independence, and made them one of the animation giants they are now. For reference, an animated film usually takes three or four years to make. Pixar films, due to their attention to detail, usually take a little bit longer. Toy Story 2 was made in nine months. Clearly, despite what the film itself says, you can rush art... at least, if you're Pixar.