Mechanical waves,electromagnetic waves and matter waves are basically three types of waves in physics.
Mechanical waves
Waves which required medium for their propagation are called mechanical waves.Transverse waves and longitudinal waves are further types of mechanical waves.
Examples: 
sound waves
water waves
spring waves
2: Electromagnetic waves
Waves which required no medium for their propagation are called electromagnetic waves.Some of the examples of these waves are given below.
Radio waves
microwaves
x-ray waves
3: Matter waves
Matter waves are the waves which contain information about the particles in the wave.