Ninpanda on 30 December 2010
I don't mind when a game doesn't have any sort of story, or only has one or two 10-second cutscenes.
I also don't mind when a game has a moderate amount of cutscenes. (Which to me is around one eleventh-twelfth of the total length.)
So what kind of a story do I prefer? A story, that is deep, intriguing and elaborate, but has as few cutscenes as possible. A story, that the player can skip, without being punished by having no idea what the funk is going on, and why the player is doing what he/she is doing.
The best (and probably the only) example of a story like this, is Metroid Prime.
