Battle of the Planets. For once, Zim is a serious threat to the Earth. Not only does Dib stop him and save everybody, he gets a Big Damn Heroes moment as he does so and even gets a slight pat on the back from one of the other Swollen Eyeball agents.
Whether you prefer Zim or Dib, "Bad, Bad, Rubber Piggy" could be a Crowning Moment of Awesome for each of them. The way Zim brings Dib to near-death or the fact that Dib was revived and put into a badass robot to get revenge.
Membrane building Dib's exoskeleton in the first place to help out his "accident prone son." The guy's rarely there for his kids, but when he is, you can really tell.
Zim reaches the peak of his awesome in the episode "The Wettening", where he flattens an entire city with a giant water balloon.
The Sad, Sad Tale of Chickenfoot: Dib sets out to expose a hoax...and succeeds.
This troper thought Zim's very first appearance was pretty darn awesome. Dude, his leaders don't even have to see him to have the crap scared out of them.
Red: That voice!
Purple: It can't be!
Zim nonchalantly telling the Tallest that he quit being banished when they asked why he was at the great assigning instead of Foodcourtia. That's right he QUIT being BANISHED just so he can attend the great assigning. You can't be more awesome than that.
"Hobo 13" is an amazing Crowning Moment of Awesome for Zim, who not only sacrifices everyone and survives 'til the end, but even WINS in the last fight. All. Alone. Cheating? How about being clever? He outsmarts everyone: horrible leader, all right, but after THAT episode he was my personal god.
GIR: You are no commander. You are a threat to the mission! Your methods are stupid! Your progress has been stupid! Your intelligence is stupid! For the sake of the mission, you must beterminated!
Zim and Dib's battle in the episode "Battle of the Planets", which is completely literal, as they pilot Mars and Mercury respectively to fight, using the entire solar system as their battleground. Special mention also goes to Zim for catapulting moons at Dib.
Gaz effortlessly and brutally defeating Zim's mecha in "Nanozim", thinking it was a video game the entire time. And then Dib proceeds to poop Zim out.
From the same episode, Tak's entire plan to hollow out the earth and fill it with sausages for the Tallest. Ridiculously awesome, and it really establishes how much of a competent Bad Ass Tak is, especially compared to Zim.
Also, Zim has a pretty major CMOA by beating Tak in an outer-space spaceship brawl with the Earth's magma flying around. Not only is it a CMOA for the animators, but one for both Tak and Zim for being able to maneuver and battle in it. Worth mentioning twice that Zim wins.
A minor moment is when Zim has his voot cruiser so damaged that he has to shoot his "windshield" into space to replace it, making him completely vulnerable to the vacuum of space before the new one is up, and then goes right back into the battle like it's nothing. It's a very small moment but it's pretty awesome.
Also his casualness as he interrupts Tak's evil monologue to shoot her into deep space at the end of their duel. He can't even bother to do his evil laugh or listen to her in the first place because he's too busy enjoying a soda.
Dib using a Humongous Mecha to destroy Zim's equally massive rampaging nanomachine exoskeleton in "The Most Horrible Xmas Ever". It doesn't matter that he is an almost perpetual Butt Monkey, this time, he won.
Another moment for Gaz would be the utter mindfuck she put Iggins through after he cheated to get the last Gameslave 2. It's perhaps the one time we really see Gaz go all-out against someone, and it's both an awe-inspiring and frightening thing to witness.
For example, his insanely awesome change into his "Frylord" suit (Complete with a multi-panel comic book screen moment), and then chasing after Zim mercilessly in one of the shows best chase scenes.
Zim's speech to Dib in Bolognius Maximus.
"THERE IS NO CURE! And I'll never make it stop! You might as resign yourself to your meaty fate! I told you you would forever rue the day you messed with ZIM! NOW! BEGIN YOUR RUING! I'll just sit here, and watch." *Evil Laugh with "Meats of Evil" playing in the background*
In the unfinished episode script "The Trial", it shows tons of never-before-seen footage of Zim's past, such as him pointing out 5 "shmillion" errors in the entire collection of the Irken database 5 minutes after being born, escaping from an underground Irk, killing 2 former Tallest, and a montage of him blowing up planets. One of the planets blew up with him on it. And it was suggested that the planet exploded because he scratched his butt. The best though is the end though, when his faulty PAK is being drained of all data by the Control Brains. However, the filtered data is so completely horrible that the Control Brains malfunction and title Zim as the greatest Irken ever!
Dib's wonderful life of doom. He fights off a swarm of fighters in space, tears apart the Irken flagship with his bare hands, jumps off, gliding into the atmosphere all the way to the ground, riding a stream of lightning, lands perfectly, accepts the greatest person to ever live award before off-handedly blocking the debris of the flagship.
Keef in "Bestest friend." Not only does the kid survive all the torture Zim puts him through, from electrocution to having his freaking eyes ripped out...but he never once loses his cheerful, sunny demeanour, and continues trying to make friends with Zim in an unproduced episode!
Skoodge gets an offscreen Moment Of Awesome when he conquers an entire planet of voracious alien rodents.
When GIR rescues Zim from the Saucer Morons. It's the only time he's been (semi) competent without being in duty mode.
Dib is sneaking into Zim's house with an invisibility suit. GIR somehow manages to detect him and splash him with a soda, shorting out his suit and exposing him.
A meta one for the fans: getting the main four of the voice cast as well as various production people to come to the first InvaderCon, even more for the second convention and Jhonen Vasquez himself, who hates traveling far for conventions. Icing on the cake for Invadercon II was the letter writing campaign to get the show back and a sneak preview of a fan animation team's production of Mopiness of Doom.
In "Plague of Babies", an army of evil alien babies invade Zim's home to take his ship. Zim proceeds to stay one step ahead of them, and quickly comes up with a plan to take them down at the last moment. It's awesome for showing that when Zim isn't given time to allow his ego to interfere with his decisions, he's actually a capable and dangerous opponent.
In the unproduced episode "The Trial", GIR conquers the earth on his own.