Elastic collisions
An elastic collision is one in which the total momentum and kinetic energy does not change (they are conserved).
Kinetic energy must be exchanged between the two colliding bodies, with no energy transferred into any other form (heat, potential energy, etc). True elastic collisions are therefore very rare.
One example of an elastic collision is Compton scattering: a high energy photon (a gamma ray), which carries momentum, but no mass, (huh?) collides with an electron, exchanging kinetic energy. Measurement of the accelerated electrons provides information about the incoming gamma rays.