I think it's very important for games like the RPG genre. I don't mind ones that lack one though, depends on the game. I like the Super Mario storylines even if there isn't that much to them.
It really depends on type of game. If it is crucial to have a good storyline, I expect something phenomianl (ex: Fire Emblem.) However, if it doesn't really NEED a storyline, it's stock drops a little (ex: Mario Party.)