If all games needed good stories there would be no Tetris.

I was obviously making a funny. :p

I don't think most people even recognize a good storyline. Some of the examples in this thread as to games with good storylines would be utterly destroyed by film critics would they be on the big screen. People seem to have very low standards for video game story's...

How much wood would a woodchuck chuck if a woodchuck could chuck wood?

A good storyline is very important to me unless it's a pick up and play game.

The best storyline in a game for me is the one from Metal Gear Solid, but I won't spoil it.

An example of games that don't need storyline but are awesome is Contra III: The Alien Wars.

Aliens invaded earth and they're surely up to no good, so you have to kill them, what else do you need?

I think story line is important in a game because if its a good story line, It makes me want to continue it

An example of a game with a good storyline but an horrible gameplay is Silent Hill 2. Damn I hated that the guy waits almost 5 seconds between every hit that he made with the pole. But still the game managed to be great and the storyline was very good although there wasn't a real explanation of what was going on.

Story depends on the game. However I have always enjoyed a really good story, but some games don't need one.