Name one example of each type of wave

A sound wave is an example of a mechanical wave.

Electromagnetic Radiation is a electromagnatic wave

Gravitational radiation is the energy transported by Gravitational waves. Important examples of systems which emit gravitational waves are binary star systems, where the two stars in the binary are white dwarfs, neutron stars, or black holes.

Matter waves are a central part of the theory of quantum mechanics, being an example of wave-particle duality. All matter can exhibit wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.