It's hard to pin down any specific ones, as the game plays out differently every time, but you're bound to experience at least a few on every playthrough.
A player who indulges in Videogame Caring Potential will find these moments occasionally. Giving higher-level equipment to Loners, traditionally the worst-off faction, as they rarely associate with each other and get picked on by bandits and bad mercenaries, can lead to surprisingly fierce fighters. Giving a couple of AK-74's to Petruha and Awl after pulling the former out of a Boiler anomaly in Call of Pripyat can lead to scenarios like finding the two having a post-gunfight meal amidst a pile of bodies, having taken down eight bandits and a pair of bloodsuckers by themselves later on. If this doesn't prove how the Zone is a badass-only land, nothing does.
In the first few missions, getting caught in a three way brawl between Military, Bandits, and fellow STALKERS and helping take out most of the Bandits and Military leaving the rest to scatter into the wilderness to be mauled by the wildife. All while having an early game load consisting of, at best, a double barreled shotgun and a terrible pistol, with only a leather jacket for protection and a few bandages.
The final assault on Pripyat in the first game certainly qualifies, with the player and a half-dozen of the most experienced veterans in the Zone fighting their way through a brutal, chaotic warzone while four different factions battle for supremacy around them.
During the battle for Limansk in Clear Sky, Scar takes down a platoon-sized Monolith force and a helicopter gunship. By himself.
Dr. Kruglov, a minor character in Shadow of Chernobyl gets one. A team of heavily-armed mercs are hunting down his team, attempting to get the data he is carrying. You can help him, but if you don't, the mercenaries will continue to pick off his team one by one until he's the last one left. Wolfhound, the leader of the mercs, will then call him up over the radio and try to negotiate with the scientist - his life for the information. Kruglov ignores him; when Wolfhound gives up and says, basically, "I've had enough. Looks like this is going to get ugly," Kruglov defiantly replies, "As you wish." If the mercs manage to kill him and you search his corpse, you find out that his last act was to delete the data so the mercenaries couldn't get at it. And there's more. If the player does choose to help him, he becomes the subject of one of the most bearable escort missions in game history, as although he calls himself a 'third-rate fighter' he's actually a fairly skilled marksman (will score headshots with any decent assault rifle regularly), and is equipped with rather tough armor. If he survives to the end of the mission, he replaces Semenov as your partner in the later Ecologist missions, and proves to be a substantial improvement over his colleague, with a better suit, better accuracy and the ability to not run in like an idiotfiring wildly at a group of zombies.
One that pops up for the player themselves for a lot of people is their initial venture down below into the sewers, in the first game, where you first encounter a bloodsucker. The weapons and equipment you have by that stage are generally poor, and that single creature is more than enough to either kill you outright or give you a big beating for a crowning moment of your own. That area forces you into a very tight, narrow corridor to get around a huge generator. You can't climb over it. You see the bloodsucker on the other side of the room. You move into the corridor expecting it to come at you in a frontal attack, but it attacks you from behind. Considering that a player is lucky if they have a barely functioning AK 74, there are a lot of tales about encountering the bloodsucker, having both weapons jam, forcing you to go toe to toe with the bloodsucker using the knife or die.
The player gets a number of awesome moments through all three games, due to being a One-Man Army and a complete badass. Spoilers ahoy.
The number of awesome One-Man Army moments in the first game alone is staggering:
The entire section in the Agroprom, especially if you didn't sneak out of the military base you surfaced in and killed everyone instead.
Raiding the military base at the Cordon in an optional sidequest for Sidorovich. Especially if you wind up doing it early on, when all you have is a double-barrel, a pistol, a duster and whatever weapons and ammo you pry off the corpses of the military guys you kill.
Clearing out the entire bandit camp in the Dark Valley singlehandedly with nothing more than a stalker suit, a stolen assault rifle and a bad attitude on your side, and feeling like you're cleaning up the Zone. It marks the turning point of the game, where you stop scurrying around like a rat and begins prowling as a predator instead.
Killing everyone in the Duty or Freedom bases (or both, if you feel like it) with at most a squad of Dutyers for support.
Turning off the Brain Scorcher, a phenomenon every stalker in the Zone bar the Brainwashed and Crazy Monolith fears.
Forcing your way into Pripyat itself, sprinting through the lead-up to the CNPP as a blowout closes in, buzz-sawing your way through dozens, if not hundreds, of Monolith troops and Spetsnaz deployments along the way. Then fighting your way through the interior of the power plant and, if you're up for getting the canon ending, the outside of the plant, where you have to go though a confusing gauntlet of portals that take you all over Chernobyl's rooftops, while at least fifty more of Monolith's very best stand in your way.
In Clear Sky:
Scar surviving not one, but two blowouts outside of protection. Nobody understands how he's still alive.
Clearing out the Swamps and Garbage of Renegades and bandits, even if the Stalkers won't get on the stick and hold the Depot properly.
Pushing through Limansk and moving into Pripyat. By then, you've gained enough ground in the Zone for Clear Sky to start acting for real.
The desperate chase through the outside of the CNPP as you try to disable Strelok's psy-protection with the prototype Gauss Rifle. Amplified by the fact that Monolith isn't helping you do it, and Scar has to survive a few ambushes to achieve his objective.
In Call of Pripyat:
The hunting missions. You'll be facing off against extremely dangerous monsters, often alone and against several of them at a time, and with a little luck and a lot of firepower bringing back word that the Zone is marginally safer.
Raiding a bandit camp instead of paying off the guys holding the friend of a couple Loners hostage.
Entering a bandit camp under the pretense of paying off Vano's debt, and then calmly double-tapping their leader and fighting your way out, taking care to grab his shotgun on the way.
Finding those lost Dutyers in the anomaly. Even if they're all dead, you've still found some missing men.
Taking the time to clear out the Monolith and Mercenary forces in Pripyat, either before or after finishing the game's main story – especially after, where (if you're very good) everyone makes it to the chopper alive, you get an I Choose to Stay moment, and are left alone with Monolith troopers flooding in and in the perfect situation for a Last Stand... which you promptly avert by slaughtering them all. Then you head back to the laundromat to rest with the stalkers that have come into Pripyat, proving that there's a reason that the USS sent Major Degtyarev in alone.
Call of Pripyat's outro. Well, if you got one of the good endings.
The up-tempo song that plays during the Call of Pripyat credits, after the ending, is pretty damn good, especially if your adrenaline is still pumping from the insane final battle. Although it's in Russian, so English-speaking players can't tell what the lyrics are.
The Firelake song Dirge for the Planet is also pretty good in the Bar area in Shadow of Chernobyl. Almost impossible to continue on your business when it comes on.
Many of the guitar songs played by various stalkers resting near camp fires. (Especially the part around 1:52-2:53 in the vid. Kickass...)
The generic "Combat" tracks in Call of Pripyat.
Many stalkers end up spending hours in the Bar just because of this.
The C-Consciousness, making it in, fighting your way through the labs, and going straight up to the site of where it all started, and if you chose to defy the C-C. Congrats, you end up gunning them down, and finally being able to leave the Zone.
The fact that The Marked One, AKA Strelok, started out with virtually nothing - a leather jacket, a low-grade pistol, and not even enough money for lunch - and a week or two later can and most likely will have changed the face of the entire Zone on his own.