Sure enough, some games have some fantastic stories that engage.
But in a lot of those games, you're playing as a blank slate. A random dude. Captain Kill, or Universe Saviour Person. But occasionally, you play as a character that you genuinely get invested in, want to see prosper, and get crushed when that character is injusticed or hurt in some way.
What was the last game you played where you really felt invested in the plight of the main character?
Double Jump Game Comics: http://doublejump.thecomicseries.com/
Surprisingly, this. I just finished the game over the weekend, and while I was impressed with the entire game, what surprised me the most was how sympathetic I felt towards the main character. He was one of the more likeable characters I've played as in a long time, especially for a shooter.
Don't post something you'd be ashamed to show your parents or your children.