Very few stories in video games actually stick with me. Even when I enjoy one, I usually forget a large of amount of plot details and instead fondly remember certain moments or quotes. And even then, those certain moments are particularly memorable because of excellent audio/visual direction. :/

That's hard to say. I like to think it would be a combination of everything, including the music (which you left out).

The most memorable games do everything exceptionally well.

These are my 7 favorite games of all time (not necessarily in any order), the games that I usually replay at least once a year.

Final Fantasy Tactics
The Legend of Zelda: A Link to the Past
Super Mario World
Pokemon Silver/Soulsilver
Civilization 4: Beyond the Sword
Super Smash Bros. Brawl
Dragon Ball Z: Legend of the Super Saiyan

definitely gameplay for me. pretty graphics are nice but will eventually be old, nice story is great but once its a replay I already know the story, the best games, the ones I want to replay again and again are fun to play just because they are fun to play.

Also for people talking about music, I love some of the music in video games but once I've heard it a few times I tend to mute it (I've played handhelds on mute since the gameboy, started because I was playing around the family and they didn't want to hear it) it's nice but again just a secondary to good gameplay for me.

Story by far.

for me its just the "feel" or "atmosphere".

i will never forget the feel i had when i turned on mario galaxy it was like jumping from a rooftop. oh that sweet pressure i had in my chests. and i play games since the early 90s. i never thought this was possible after so many years of gaming more than 20years to be precise.

Story and setting for the most part.

However, I also think that the most memorable games are those that manage to gel storytelling and gameplay together, where the story is told via the players interaction and actions. Think Shadow of the Colossus, Deus Ex, Knights of the Old Republic, Mass Effect, Bioshock Infinite or Half-Life 2. Stories told via setting and gameplay.

For me it's the story i remember most. I don't care so much about graphics as long as they are good enough for that particular game. Like the last of us, it would of been good on an older platform but because it came on current gen, the graphics were there to help the story be even better especially in it's key moments. Gameplay also helps with the story as does the soundtrack. The best games usually put effort into all 4 areas.

Graphics.

People are obviously going to jump on the "GAYMPLAY NOT GRAFIX" bandwagon, but in the end, it's what you see on screen that you remember. Everything from art style and the way the world is constructed to menus and interfaces.

why is its soundtrack not an option, easily the most memorable part of a game

Story, no doubt for me. That's why The Last of Us will remain with me for a long, long time.