What is conserved in a collision?

First of all, consider what the word "conserved" means.  A quantity is conserved if its total value does not changed.  For example, in a chemical reaction, mass is a conserved quantity -- though one reactant might seem to disappear, if we carefully trap all the reaction's products, we find that the total mass before and after the reaction is the same. 

Momentum is conserved in ALL collisions.  (This means that the TOTAL momentum, including all objects, is the same before and after the collision. 

Velocity and force are not conserved quantities in anything that I am aware of.

Kinetic energy is usually NOT conserved.  Only in the special case of an "elastic" collision is KE conserved.  In an elastic collision, the objects must bounce off each other.  However, the converse is not true:  the fact that objects bounce off of one another does NOT mean that the collision must be elastic.

A frequently asked AP-style question (as on 2008 B1) gives details about the collision, and then asks whether the collision was elastic.  Usually the solution entails using conservation of MOMENTUM to find the velocity of each object after the collision, then calculating total kinetic energy before and after the collision for the comparison.