I agree with Jacanuk. To answer your question, though, it depends on my mood. But in the long run for as much as I like a game like Ikaruga, gameplay will never leave you "haunted" like a good story can. I've seen movies that were literally nothing but dialog that stuck with me for long after they ended. There is no equivilent in terms of pure gameplay.

-Byshop

I'm not sure. When it comes to videogames my story expectations are relatively low, since I feel books and films are still much better suited for telling a story (which does not include certain external factors that videogames offer that might make a story have a stronger impact on you, like being able to control a character's actions or to experience the narrative world more directly). Books and films don't have to compete with gameplay and generally offer much more depth and development.

So I would say story in videogames is important (depending on the game, of course), but I do not have the same expectations as with films and books, so on some level it isn't that important. I'm very forgiving when it comes to videogame narratives. But maybe I shouldn't be...

Story is the main thing I look for in a game, but obviously only certain types like rpgs, fps single player games and open world games.

I don't need a story in a racing, sports, or online shooter game.

The games I enjoy most are ones with a great story, I'd say it's pretty important. I'm less likely to finish a game with a weak story.