A very interesting topic, that really got me thinking. As TimovieMan said, we're all different and so are developers. That's why there are different games for different tastes.
For me personally, the more story the better. I've let that known here in every other post I put up probably
That's not to say I don't like minimalistic approach to storytelling. Myst, Ico, Shadow of Colossus I loved as much as say Metal Gear Solid 4 which has 30 min cutscenes. If the story and atmosphere is good, I'll play it, no matter what the genre. Gameplay just needs to support the story as Annacat pointed out. You can't make an adventure game out of an up and coming race driver for example.
I do tend to lean more towards games that can be called interactive movies however. I tried to get into all-challenge-no-story games at one point, 'cause everyone raved about those and couldn't get into them. For me it was pointless chasing the next high-score, it didn't give me anything. A good story driven game fulfills me much more.
I'm polar opposite to Oscar, whenever I want to watch a movie, I'll play a game and take part of it
