Snake-Eyes is awesome personified, including breaking into Destro's castle to save Scarlett and actually taking on Storm Shadow and his ninjas with little weapons, and breaking free during a Cobra torture session, and going upstairs to rescue the people who were supposed to rescue him. In Snake-Eyes-Land, prisoner saves you!
The comic introduction of Duke and Roadblock. Cobra Commander sends a prototype Rattler to strafe the Joes during Gen. Flagg's funeral. Duke and Roadblock show up out of nowhere and shoot it down using only a .50 cal and a pistol.
In issue #28, some Joes on the WHALE face Destro, who attacks with a Rattler. Then Roadblock's gun is eliminated and Deep-Six's mount breaks. The Rattler keeps coming so Roadblock uses his own back as a mount and Deep-Six destroys the Rattlernote Destro ejects before the Rattler is destroyed, though.
In issue #34, we have Ace in the Skystriker with Scarlett facing off against Wild Weasel in the Rattler with Baroness. The awesome part comes at the end, when they face each other head on, only to realize they had run out of weapons. As they pass each other, they give a salute, and fly off back to their respective bases in their trashed planes.
Issue #80: The Rolling Thunder is facing off against several Cobra Maggots, and beating the hell out of them. The crew of one of them gets the bright idea to try to get close to get underneath the Thunder's main gun. It works... until the Rolling Thunder runs them over.
The opening for the 1987 film is made up of several of these. Examples include Snake-Eyes stealing a Trouble Bubble in mid air, Cobra Commander getting punched off the statue of liberty, Alpine swinging out of nowhere to kick open a Firebat's cockpit and Duke blowing up the Cobra airship.
The opening IS a Moment Of Awesome when you boil it down. As one Youtube commentor put it: Ok. So let me get this straight...It is the 4th of July and a terrorist plants a bomb. Then the G.I. Joe grabs the BOMB while wearing a jetpack, BLOWS UP the terrorist's main ship, PUNCHES through a jet cockpit, and PUNCHES the terrorist leader off the freaking Statue of Liberty. Then one of them lands and plants an American flag on the Statue of Liberty.
When a "best of" DVD of the animated series was put out, the opening was included. Not the movie—just the opening.
From the 80s cartoon, the episode "Nightmare Assault". Dr. Mindbender has invented a machine that allows him to give the Joes nightmares to (a) disrupt their sleep and make them less effective in the field; and (b) create opportunities to Mind Screw them by re-creating nightmare imagery in the real world. Then he turns the machine on Low-Light, who's already prone to nightmares (unresolved father issues, it seems). Turns out, the machine's nightmares are so weak compared to Low-Light's standard fare that he's not only able to overcome the device and help his teammates do likewise, but he actually makes progress with his own nocturnal terrors.
Low-Light: You gotta be tougher than that. I'm not a wimp anymore! I'm a G.I.Joe - and nothing stops a G.I. Joe! NOTHING!!
To top it off, he makes sure Mindbender gets Hoist by His Own Petard when in the process, Low-Light ends up giving the Doctor such a scare through the machine that Mindbender destroys it, having seen this was too much even for him.
The climax of the five-parter "Arise, Serpentor, Arise!": With Serpentor as its new leader, Cobra stages an assault on Washington DC and, in a frightening display of power, seizes the city; Serpentor declares himself the emperor of the nation. This is all following on the heel of several episodes where Cobra managed to outmaneuver G.I.Joe. G.I.Joe's response? Infiltrate the city and proceed to open a can of whup-ass on Serpentor and his forces. The next few minutes of battle that ensue make for one of the most woot-worthy action scenes in 80s Western cartoons.
Just to be clear, they infiltrated the city by disguising themselves as the president and other American politicians, claimed to surrender and then revealed the deception right in front of a very surprised Serpentor.
Earlier than that, Sgt. Slaughter took on Serpentor one-on-one and won.
Cobra Commander has a few depending on the version:
"Arise, Serpentor, Arise!" has him as the ironic Savior of Serpentor, when a flamethrower stream stops the Joes from advancing on the Emperor, and it's shown the Commander was the one who fired it.
"GI Joe vs. The Transformers" had him at the end of Volume 2 also admit he lined the housing of a traitorous Starscream with 45 pounds of plastic explosives. Which detonate and take out the top of a Decepticon tower that had Starscream, new Decepticon leader Shockwave, and a few other Decepticons too. Ironic in that Cobra Commander finally brought peace back to Cybertron with this act, a fact which probably would've annoyed the heck out of him if he had been aware of it.
And in part 3, he manages to size control of Serpent O.R., and by extension the Matrix, all the way from back on Earth.
Roadblock in regular continuity: A US embassy is being looted. A guy screwing with the American flag gets Roadblock's huge machine gun up his nostril. Roadblock indicates that if he harms the flag, he will lose his head. Guy points out people stealing office equipment. Roadblock: "Nobody ever died for a typewriter."