1. Solids: Waves can travel through solids as both longitudinal (compressional) and transverse waves. Examples include sound waves traveling through a metal rod or seismic waves traveling through the Earth.

2. Liquids: Waves can travel through liquids as both longitudinal and transverse waves. Sound waves traveling through water and water waves are examples.

3. Gases: Waves can travel through gases as longitudinal waves. Sound waves traveling through air are a prime example.

It's important to note that:

* Electromagnetic waves are a special type of wave that can travel through a vacuum (the absence of any matter) as well as through mediums. Light, radio waves, and X-rays are examples of electromagnetic waves.

* Transverse waves need a medium to travel, while longitudinal waves can travel through both mediums and a vacuum.