Mexico is one long Crowning Moment of Awesome for John. Not only does he manipulates both the Government and the Rebellion in order to get his objective, he also manages to win some of the biggest shootouts in western history. He's pretty much the one who decides who wins the war at the end, even if he doesn't care.
Except for that one time he almost gets executed for betraying the government. Then it's a Crowning Moment of Awesome for the Rebels.
Certain times of day make this mission (among others) even more awesome. Setting off from Macfarlane's early in the morning, meeting up with Irish just before dawn gives a real sense of going on an adventure to a foreign land. Fight through the sunrise, then head off to Chuparosa with the sun behind you and Far Away playing.
The surprise credits after "Remember My Family".
John riding to reunite with this family while the epic and touching "Compass" plays.
Landon Ricketts dying in his sleep. Might not sound like much in the grand scheme of things, but consider the fate of all the famous gunslingers of the West (Billy the Kid, Wild Bill etc). They were all murdered by someone else. With Ricketts the only thing that could kill him was time itself.
The Assault on Fort Mercer. Sure, it's not really far into the game, but seeing Marston pop out of Dicken's wagon with a gatling gun and absolutely lay waste to dozens of mooks definitely belongs here.
It can be immensely enjoyable to don a duster coat, pick up a 6-gun, and turn on infinite ammo, health, and Dead Eye cheats in order to walk around role-playing the Saint of Killers.
Random encounters can easily become awesome depending on the player's actions. But the coolest has to be when bandits attack a town and you stand out in the middle of the road as they come to you, whip out your revolver, activate deadeye and headshot each bandit off their horses staying still as the horses run right past you while your duster coat blows from the wind of the running horses. As a bonus the guy they were dragging and the townsfolk will thank you for such an awesome display of badassery.
Random happenstance can turn many of the games moments into cinematic triumphs. For example, it's completely possible to duel Edgar Ross, during a thunderstorm, in the middle of the night, as wolves circle you both.
Using Dead-Eye and dynamite/Molotov Cocktails to create flying explosives that hone in on targets with no plausible explanation.
Meta-example for Rob Wiethoff. Despite it being his only video game role ever, and one of the only acting roles he ever had (especially since he retired from acting shortly after), Wiethoff's performance as John Marston is regularly listed as one of the finest voice acting performances in gaming history, being placed near the top of many "Best Ever" lists for voice acting.
Managing to kill a cougar, especially in multiplayer mode, where they can One-Hit Kill you. There's a reason cougars are such a memetic badass on Gamefa-*COUGAR'D*
A small one, but when John first walks into the sheriff's office and tells Jonah he's from Fort Mercer, Jonah reacts by reaching for his gun. When John notices this, he pulls his gun out twice as fast and is already pointing it at Jonah when the former gets his out. Only took a split second to show that difference in experience.