As a gamer it is almost always the story-line that pulls me into the game and makes me want to play it a million times over even after I've completed it. It's the same as a book where you know exactly what will happen but you still get a thrill from reliving the excitement of discovering the plot and learning more about the characters.
The majority of games I play are RPGs/action games, which are pretty
much meaningless if there isn't a decent story to follow. I personally find the storyline for Zelda: Link's Awakening particularly compelling. It is a GBC game so the graphics are okay for a handheld but I guess this is what a game needs when other aspects are lacking. Saying this, looking at the graphics of the ps3 or xbox360, as breathtaking as the visuals are i'd rather play a nintendo console anyday just because the storylines tend to be more involved and make me actually want to play the game.
Another example of the importance of storylines in gaming is to maintain the players interest. Obviously not all games have a story though, arcade games such as the original mario series didn't have much of a story to go by (defeat bowser, save princess peach...) yet this didn't detract from the gameplay which was basically just plain addictive. I think I prefer games with more depth to them as it makes the experience more realistic.
I think the reason some games at the moment aren't so great is because the stories have lost originality and impact, there are a lot of games out there (3rd party games in particular) that just have no passion whatsoever and they're just boring to play.
In the Harvest Moon series you create your own story for your character, it is the choices you make that determine certain aspects of the game, with there being many variables in the game in how you decide to spend your time each day such as how long to spend on livestock, planting vegetables etc.
My favourite story line is in the Sword of Mana, there are a lot of characters and I found it interesting how they all turned out to be linked. You can tell a lot of thought went into the story, with there being a choice of which perspective you can follow- at the start of the game you can choose to be either the male or female character, but depending on which you choose takes you on a different route in the game and it's really interesting to discover how these two seemingly separate stories are actually entwined which is what captivated me about this game.
See ya ~Emi ^o^