Nothing deeper than "You are a hunter, kill stuff" ^^
Hm, the Stories that I enjoyed more than others:
Devil May Cry 3 - The story was pretty amazing in DMC3 (for the series), it was simple, captivating and kept you smiling throughout -- it actually made you care for the charcters (Dante, Vergil and Mary) rather than ignore them (DMC 1 + 2). Devil May Cry 4 was a better story too, just not as fun for me compared to 3.
Star Wars: The force Unleashed: I thought that the story was very creative, fitting neatly into the established canon and giving you people to care about, plus you got to experience both sides of the Force. The DLC was fun too, extending the original plot and giving a whatif scenario to the Evil ending which TBh was fun too -- kicking Lukes @$$ FTW!!
Legend of Zelda - Majoras Mask: I thought this plot to be far more creative than current or previous Zelda games. The introduction of Masks gave the game a far greater depth than OoT, it's as fun a story as Wind Waker which is another Zelda game that captivated me! Only 3 Days to stop the Moon crashing into the World? Such a great story! ^^
Pokemon R/B/Y: While this has been done to death since R/B/Y, the story of a young trainer wanting to be the greatest Pokemon whatever ever kinda related to me when it came out. Collecting all the beasts and searching every nook and cranny for new and more colourful creatures didn't get boring until the most recent games. (Hopefully this will be revived when B/W arrive), it was a great game, with a simple story, it worked for me ^^
Final Fantasy IV - I think it's original number is III, but I'm referring to FFIV on the DS with Cecil and Kain. I loved this game, and it was a plot that held nothing back, love, battles with a darkside, rivals, friends, comedy, it has everything and I adored every moment with that title and it was the story that drove it. Alike Final Fantasy IX it just wowed me from the opening scene! ^^
Infamous - While cliche'd, it was a great story. Simple and fun, but with such a dark twist at its conclusion that you cannot help but be stunned! EPIC! ^_^