When it comes to Japanese RPGs, story is indeed very important and the characters are to. When it comes to turn based RPGs, the enjoyment is based on the story and characters. In Western RPGs, story is not as important but that does not mean it can't have a good story i.e. Mass Effect

I actually rate Story as the most important thing for a single player game for me to enjoy it. Which is probably why I enjoy JRPG's so much. That's not to say that Gameply is unimportant, it's just not quite as important for me as story is. A game with great gameplay and a bad story is enjoyable, a game with bad gameplay but a fantastic story is something I will come back to again and again.

In certain games yes.

 I completly agree, Story for most games I find is essential, other wise i find it boring, gameplay is a massive part as well, these days im afraid graphics are overrated and no were near the most important thing for a game to be good.

if its a single player game then yes the story means everything.

if its online i care but not that much.

sometimes the story can even motivate you to copy things from it in real life like metal gear solid 2, it did for me.

it also adds good replay value to the game if the story is good.

I actually strongly dislike story in games, and consider games that are heavy on story to typically be my least favorite type (I don't play RPGs often or at all, for example). I am heavily focused on games that are skill based; this almost always means multiplayer, but I give games like Ninja Gaiden a whirl (enjoyed Sigma on PS3, although I had to wince every time the trite, heavy handed story line took center stage) and particularly puzzle games like Echo Chrome (love it) and Professor Layton.

Anything that tests my skill and allows me to compete with friends. 

I love stories in games. They really help me get into the game more, and they add a lot to the experience.

for me only the story matters, I dont care about gameplay much. so story matters a LOT.

i pick story over online play any day, i can be glued to the tv if the story is good enough, but in online play, i tend to lose interest after an our or so.