Why won't the pivot point/3D cursor move to center of object anymore? When I started using Blender whenever I clicked an object the pivot point would immediately be at the center of whatever I clicked. 

Now it just stays where it was last put and doesn't move until you manually do it.

How do I fix this?
You have you piviot point set wrong, try , on your keyboard:

In red is what you have it set to, in green are options that will achieve the result you want