WHAT MAKES A GAME'S STORY MEMORABLE TO YOU?

For me the most important are the characters and how they look live at the game. Also the atmosphere created using the visual, and especially the sound effects is always very striking. Plot twists are also striking but only affect the player who is already feeling in the world created by the maker.

The characters. If I love or hate the characters I'm going to remember that game. For example, one of my favourite games is Suikoden II - I loved (and some, hated) the characters to bits. Flik, Victor, Nanami, Jowy, Riou, Theresa, Luc, Killey, Clive, Culgan and Seed... You get the idea. Also Luca Blight, you mad, magnificent bastard, oh how I love killing thee. >:D

Other times it may be the art direction combined with great characters and gameplay - Okami for example. Yeah, just Okami actually.

And sometimes I just have no idea - Oh Legaia! Why do I love thee so? Your characters aren't that great, your battles get annoying after a while, your bosses kick my ass... and yet, I think you're grand~

I need to be able to feel what the character feels. If I can't become intune with the people whose lives I am supposed to be getting to know and understanding, then what about that game is there for me to remember?
Q: "Oh, remember that game with those awesome gameplay mechanics?"
A: "You mean the one with the emotionally dead and detrimentally pointless characters? No, not really."