D1 had no story at all. There were a handful of cut-scenes that were loosely related to each other but that's it. There was no cohesive narrative, no character development, a generic "darkness" instead of an actual antagonist. D1 was criticized quite heavily on release for its "story", or lack thereof, and rightfully so.
Now if you are referring to lore (which is not the same thing as story) then I might agree. There was a lot of lore left over after they tore Staten's original story apart. They gave that to us as the Grimoire instead.
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<I guess the Darkness will still be a generic thing when D3 rolls around. Unless they give IT a personality it's going to be a faceless thing commanding a fleet of unstoppable ships.>