Stories in games?

As a gamer who's played everything from pong to the latest and greatest, I've really begun to enjoy the stories in video games. Andrew and I like the stories in games but Ashley couldn't disagree more. She says that if she wanted a story, she'd watch a movie. She's more of a puzzle gamer and I jokingly act out the story of the purple jewel in bejeweled. He came from the unholy union of a blue and red jewel who met across a crowded board. Two lonely jewels who met at just the right time. She just laughs and rolls her eyes. So I'll ask the question to my readers. Does the story of a game make any difference to you? Do you seek out games with a great story or do you prefer mindless fun where you don't have to focus on characters?