The Old Republic has a lot of different types of quests that make up the entire story of the game. All of these will interweave to make up your final play experience.
Your 'Class Story' is the storyline that specifically relates to you as a Jedi Knight, Bounty Hunter, or whatever you're playing. Quests that advance your class story in important, decisive ways are instanced. During those instances (which are generally short, and do not make up the majority of the game world) you get to make story-defining choices. If anyone else is with you in that story instance, they do not get to make choices that would affect your story. (In fact, they can't even enter the instance unless you're grouped together.)
Outside of Class Story instances, we have World Quests, Flashpoints and Heroic Quests. In those, if grouped, your choices will be dictated by the decision the group makes. So, to put it bluntly, if you never want to see a decision taken by someone else - well, the final solution is to not group.
That's kind of extreme, though, and we want you to group because that's part of the fun of any MMO. So, the choices that are presented to you in Flashpoints, for example, are not so critical that you should ever feel your entire game story has been destroyed by one dice roll. (However, you should hopefully enjoy the unfolding story that may go some interesting places due to other players. That's the fun of an MMO.)
Your over-arching Class Story, which has the most critical set of decisions you'll make in the game, is never affected by other people. That's a deliberate design decision, to ensure that the 'big moments' in your story are guided by you and you alone. Here you truly are 'Master of your Story'.
