Gameplay and story. One of them has to be good, or more accurately, one can't be bad as if affects the other's delivery depending on the title. Graphics are great. The improvement of graphics allow for better gameplay and better storytelling. Think the jump from 2d to 3d as a great example of graphics giving games a lift.

Generally I would say gameplay>story>graphics (though I would also say art direction is more important than simply graphics), but it really depends on the type of game. For example, in fighting and sports games you can throw story out the window but an rpg with a horrendous story is almost unplayable even with good gameplay.

Story > gameplay > graphics.
I need to feel an attachment or emotions for my cast and their motives. I like "realistic" graphics over cartoon but I don't mind if the story is compelling.

Gameplay > EVERYTHING

Games are for gaming. The story and all that stuff is the support, like the music is the support of the cinema, but never the focus.

Gameplay> Story> Graphics

Gameplay > Story > Graphics

...

Gameplay and story are tied depending on the game. Graphics are third.

As little as I value graphics I'd probably still chose that over story. Obviously gameplay is the only important factor as some of the greatest games of all time has no story at all and incredibly shitty graphics.

I have from time to time played so called 'story driven games' and they have all been, without failure, miserable experiences.

Gameplay by a mile! Most of my favorite games of all time have limited stories. Some have great graphics some don't. They all have essentially perfect gameplay.  Level design is another thing that is very important to me in great gaming.