I want the opposite. Sod the story - give me a focus on variety and gameplay. I can think of one game that gripped me from start to finish due to the quality of it's story telling. Planescape Torment. Everything else is straight to dvd action/sci-fi/fantasy. All we need is a bad guy and an objective and we're good to go.
The problem is developers trying to emulate movies rather than giving us games that are about playing with stuff.