Will I visit all the explorable zones if I follow the personal storyline to the end?
The next mission is going to take place in a new zone, and I'm split between completing a nearby zone now, where no mission has taken place so far and I just happened to wander in, or coming back later if the personal storyline is going to take me there eventually.
My race is Sylvari, if that makes a difference.
No, you will not receive missions for each zone with your personal storyline. Which zones you travel through will depend on your race and the decisions made during character creation and during your storyline.
I recently completed the personal storyline, and found roughly half a dozen zones that I had never been to.