What is the motive behind the Titan Shifters' actions? Okay, so I read a bit of the manga, and I know a good amount of spoilers. But why are most of the titan-shifters trying to destroy humanity? Eren and Ymir are good, right? Why do some titan-shifters want to destroy humanity, and what are Annie's, the Colossal Titan's, and the Armored Titan's backstories and motives?
Since there isn't much revealed in the manga, this answer is going to be a speculative one.

It's known that the royal family has been trying to wipe out the titans. They prepare someone to become the "Carrier" of the Coordinate, but each time a new titan gets the power, they accede to the demands of the 1st king, that is to allow the titans to dominate human, i.e. Titan rule.

The primary motive of the Titan Shifters is to recover the Coordinate, unknown to the fact that only someone from the royal family can use it's powers optimally. 

This leads me to think that


The ape titan, is somehow related to the royal family and wants to fulfill the 1st king's wish.
Or, he just wants to convert all humans to titans, thus creating an only titan nation and annihilating humanity.