A day or two ago I saw this thread on the DND subreddit. It's an awesome story about the events at one person's table where he got a truly heroic moment out of his players and a noble sacrifice that will probably remain with everyone there for years to come. In talking about it with some friends, we all agreed that they were the kind things we love about gaming, but also noted that in certain games you just never seem to have them pop up.
The thing we didn't discuss, the elephant in the room so to speak, is that there is only one way to get great moments like this: everyone involved has to be invested in the game, or these moments can't occur.
Consider the story in the thread. You have two players who have invested into their characters. The gnome player has gone out of their way to invest in a quirk for their character - they don't like their height coming up in a way that implies it is a hindrance. They have played this quirk time and again. They have likely caused trouble for the group over it, had discussions over it, and it was done so thoroughly that per another player's own admission the thought of picking up that gnome never even occurred to them.
The other player is the paladin who clearly is invested into who her character is, but also cares about the character enough that she's sinking money into them for a miniature and commissioned art and the like. These two players both feel for their characters, and that is why this moment works. It is why it is tragic. It is why it brings a tear to the eye.
Without the investment this scene plays out differently. The paladin picks up the gnome, and they just run. The gnome player bickers, but ultimately doesn't do anything because why would they? Alternatively, the paladin leaves the gnome behind. Or maybe the paladin still saves the gnome to their own peril, but it doesn't have the same impact.
I look from that to two of my own characters. In an online D&D game I play a Dragonborn Battlemaster named Rhogar. I like Rhogar a lot, but I am not super invested into who he is as a person, and in combat I am prone to throwing Rhogar into the thick of things not just because that is who he is, but because...well...who cares if he dies? I like the character, I like the game, but I am not fully invested into the character. If Rhogar died, it would be sad, but it wouldn't be devastating for the group. We're all grizzled vets who have seen countless party wipes and as such have that distance built in.
At the same time, in an L5R game I am in I play Mirumoto Rei. If Rei died well, I'd be fine with it - because Rei would be fine with it. But if she died some cheap death? I don't know. I also think that if she died in a way like the story I linked above, it would have similar impact. Unlike with Rhogar, I am heavily invested in Mirumoto Rei. I have written at least a dozen short stories to fill gaps in time for the GM with what the character is doing. I have developed her personal life. I know what type of people she likes, what type she dislikes, what she finds attractive, favorite and least favorite foods, the whole bit.
Rei is a fully realized person. Rhogar is a character in an RPG played by an experienced player and story teller. There are countless reasons for this discrepancy from GM styles to game styles to number of players to my comfort playing with said players on an emotional level, and none of those are bad or wrong. But in the end it boils down to how invested I am in the character.
I like Rhogar, but I don't know him.
Mirumoto Rei has real-estate in my brain where I don't even have to consider what she'll do, I just know.
Unsurprisingly, Rei has had more great moments. And I think the same is true in every game. The characters with the most investment in them are the ones who get the moments that define the game.