When I press on the brakes the rear end on my car shakes can anyone tell me what's up?

 

Warped rotors would be my first guess.

 

I'd say that too if it weren't a base model car, which means it probably has drums in the rear.

 

Drums can be out of round too. The shoes could be sticking as well. Could be hanging up on the backing plate. If the axle seal is leaking that can cause issues too.

OP, a little more info would be helpful. Does it happen at all speeds? Is it just the rear end that feels loose? Drums or disc out back?

 

How are the struts up front; could the car be diving to the point that the backend is skittish? Hard braking or light braking?