I think story is an important element when they try to use plot. I don't necessarily think then it has to be Shakespeare, but it needs to be suitable. If a game is only using a plot just to move the game in a direction and it's all really just about the action, then it doesn't have to be anything substantial. When a game is using plot as part of its focus - particularly with an RPG as it comes with the territory, then it needs to be good, otherwise I just find myself lost.
Also, when it comes to dialogue, it would be nice if it was well written dialogue.

I've played good games that's had bad dialogue, but felt it was slightly ruined by it...not completely though, some games I've added subtitles and either turned off the voices or (if possible) changed the language settings, case in point, Star Ocean 4, I played it in Japanese with English subtitles.