Anytime you use a Fat Man and watch the glorious explosion afterwards. Especially if your first time is the Super Mutant Behemoth attack in the Galaxy News Radio station, with the Brotherhood's best watching you in awe as you, a random wastelander, blows the giant to kingdom come.
And the MIRV is a Fat Man in shotgun mode.
The Experimental MIRV classes as a Gun of Awesome. No matter what you decide to use it on, it always leaves your mouth watering.
As the name implies, testing the weapon in different situations in the game and launching or even glitching your own character by firing into the ground turns The Experimental MIRV into it's very own Sidetracked by the Gold Saucer.
Everything and anything with Liberty Prime in it, especially the first time you see it. They tell you that you and your allies will be leading the assault and the robot will be sent as back-up. Nuh-huh, the robot is leading the assault and your job is to find a good spot from which to view the epic Curb-Stomp Battle. Nothing stands in his way, or at least it doesn't stand for long before he blows it up.
Probability of mission hindrance : ZERO PERCENT! Battle analysis: Red Chinese Victory IMPOSSIBLE! Democracy is NON negotiable! Embrace democracy, OR YOU WILL BE ERADICATED!
Consider how long it took you to cover that kind of distance in the Capital proper earlier in the game, and behold how Liberty Prime strides unchecked through the heart of the city, straight up to the purifier complex, plowing through dozens of Enclave troopers like he was walking across the street for a loaf of bread.
Paradise Falls is widely regarded as one of the best gunfights in the game.
Any video where "the annoying man" gets executed is both awesome and hilarous at the same time. And even though you said agreed to escort him, you don't lose any karma at all if you kill him!
Fawkes in general. Not only was he planning on breaking you out of the Enclave base with a Gatling Laser he apparently got hold of in a few hours for that express purpose, but he's also capable of taking down nearly anything on his own.
At the end of the Broken Steel quest "Who Dares Wins", you get to launch an orbital strike on the Enclave's airforce base! This is, of course, after you fight your way through the entire base full of Enclave troops. The most satisfying moment is when you realize just how royally screwed they are now after causing you and the wasteland so much trouble.
Managing to find and put together all the junk you need to create all of the makeshift weapons like the bottle cap mine or deathclaw gauntlet, then testing them all out on a group of raiders or other annoying foe. Nothing beats killing Demonic Spiders with the random trash you find lying around the wasteland.
Particularly so for the Rock-It Launcher. Is there anything more rewarding than slaughtering your foes with the cuddly wuddly death of a thousand teddies?
The finale of the Mothership Zeta DLC, where you engage in a space battle with another alien ship, especially when Sally treats it as if it were the climatic finale of an epic sci-fi TV series/movie/videogame.
Going to Old Olney armed with nothing but a Dart Gun, a Chinese Pistol, and a huge stockpile of 10mm ammo, and proceeding to Cherry Tap the Deathclaws into oblivion.
Argyle killing Penelope Chase, the former leader of the slavers:
Penelope Chase: Don't try anything funny, zombie.
Argyle: Why, Miss Chase, there isn't anything funny about... THE EAGLE CLAW!
There's something poetic about taking out Enclave soldiers, equipped with the highest level of technology, with jury-rigged Wasteland weapons like the Rock-It Launcher, the shiskebab, or the Nuka-Grenade. Imagine a soldier dragging himself back to Col. Autumn, having to explain that his squad just got annihilated by a can of soda and a high velocity teddy bear.
Killing Mr. Burke before he can shoot Sheriff Simms in the back.
Dogmeat with the Broken Steel DLC is just amazing. Due to a glitch involved with leveling up, he has his health rise exponentially every time you gain a level. Assuming you found him early in the game, this means you can send him up against a veritable Supermutant Army on his own, and watch him come out with nary a scratch. At level five. Add on the Puppies! perk, which allows Dogmeat to respawn as a younger version of himself outside Vault 101, and you have a companion to be reckoned with.
If you got the Point Lookout DLC and got the quest to destroy the book in the Dunwich Building and you do so. After some Fridge Brilliance and a little thinking it hits you. You just destroyed the Necronomicon. You did what thousands of Call of Cthulhu investigators failed to do.
Watching James punch out deathclaws with his bare hands.
Or if he decides to skip over all the assault rifles dropped by raiders and instead pick up a sledgehammer.
Near the end of Broken Steel, you use the train in the Presidential Metro to get to Adams Air Force Base. After trekking through every subway system in the Capital Wasteland only to find out that the War did them in and rendered every train line unusable... and after using a handcart to travel to the Pitt... it's a refreshingly breathtaking moment from all the ruins you've seen everywhere in the wastes to have a fully functional train to ride in200 years after an apocalyptic war.
Completing the quest "Stealing Independence." Having fought your way through the hordes of Super Mutants in order to save the Declaration of Independence, you may come to the conclusion that this really is much more than just a piece of paper. Thousands, nay millions, have fought for the ideals it stands for. You are now one of those proud few.
Burke's an asshole, sure, but when Roy Phillips tries threatening him after his successful clearing out of Tenpenny Towers, he threatens Burke with the same fate as everybody else... but Burke merely threatens him back, and Roy starts back-pedalling and offering to make him his Number Two.
Towards the end of Mothership Zeta, by going off the beaten path, you'll find Toshiro, the Samurai you freed from cryostasis, surrounded by dead aliens. Then during the finale, Sally lets him into the control room where he proceeds to annihilate every wave of Aliens who storm in soon after.
Even better, if you help him along with the cowboy and the pre-War soldier. Think about it: The samurai, the cowboy, the pre-War soldier and you represent different periods of human history, and you are all destroying the alien invaders as payback for the centuries of abductions. You're all sending the aliens a message, and the message is "Humans Are Warriors". Showcased beautifully with the name of the last mission: The Galaxy Ain't Big Enough...
Hell, playing the game for the first time and hearing the menu music is a CMOA itself. It leaves quite an impression.