It's the classic chicken or the egg question. Just how important is proper writing to a game's success? We've all played great games which functionally had no story (Super Mario Bros, Rock Band) so it's not an absolute prerequisite. But in this day and age, most non-sports games are assumed to need a story and dialogue. Because the converse is also true, we've all also probably played a game where you just can't wait for that next cut scene, that next story twist.
Now under consideration:
Best Game Writing
The Nominees:
Braid, Call of Duty: World at War, Dead Space, Grand Theft Auto 4, Metal Gear Solid 4: Guns of the Patriots & No More Heroes