Depends heavily on the game. When I play an RPG or an Adventure game I want some kind of story, but a heavy story isn't necessary. I'd much rather have a light, well told story than a heavy but terribly told story when playing RPG's though. When story is one of, or the main driving force it needs to be good or I will get bored, stop playing and neer touch the game again. That has happened to several RPG's I've played. I don't think I would want to play an RPG with no story at all.
When it comes to casual games such as Tetris or Plants vs Zombies, I want as little story as possible. I play these games when I just want some mindless fun and a stronger story element would completely stop me from playing them.
Same goes with most platformers. I don't want lots of dialogue. I just want to play, nothing else. Heck, I played through Donkey Kong Country 3 yesterday and the few lines in that game annoyed me, and while I think games like Ratchet and Clank are great they contain way to much talking for my taste. This is just imo, of course.
None of the poll choices really suits me so I won't vote, but I guess I stand somewhere in between the "Story = Waste of Time" and "No Story = No Game" camps. There are certain genres where a story makes for a better experience, and there are genres where forcing a story on the game would be pure stupidity. If any of these extremes were true for all games it would severly limit my enjoyment with games, and I would not be the gaming fan I am today.