In the single player campaign, the player will have his/her own unique story. The choice of missions, their order, and the choice of discussion items with NPCs will provide a number of different outcomes.
My experience in these "choose your own destiny" type games is that each subplot tends to be rather shallow. At blizzcon, it was explained that the game will follow a football arc. Players will start from the same position, but will also find themselves reaching the same end game experience. Similar to starcraft 64.
It seems to me that it will be difficult to have an intricate plot throughout the game -- but that is not to say that it will not be done. At least in starcraft 2, character interaction won't be restricted to bickering at each other in the mission briefing room.