I feel that the storyline is absolutely essential to any game. Without a storyline, what is the point of a game in the first place? I think that the more realistic the storyline is, the better and more realistic the game is; for example Halo- it actually does have a pretty in-depth storyline, but the game play is quite generic, a first person shooter, running around blasting the aliens. I feel that it is a very overly hyped game when games like Uncharted, Bio-shock, Final Fantasy and Metal Gear Solid have taken storytelling to a whole new level- or if it is too easy, it isn’t much of an accomplishment when you finally finish a game. Also the characters in the game are very important too; if you can connect with the character or relate to them, you can become immersed into the game.
“Emotioneering” is a term created by David Freeman, which was to describe a body of over 1000 techniques for making a game emotionally immersive. That is, they evoke, in a player, a wide breadth and depth of emotions. The emotions in the storyline are what integrates a story together; and it can make a game go into a more significant depth, or make it crash and burn. Also originality in a storyline is important; you don’t want to be playing one game one week, and a slightly altered version the next week- diversity is what is desperately needed in games nowadays!
I know I am talking about Eye Pet waaaaayyy too much, and also Little Big Planet; but I am only mentioning these to make a point. These games don't have a storyline per-se, but they show my point of how the character can add the same quality as a good storyline; as well as originality.