Elements:

* Oxygen (O): Makes up about 21% of the Earth's atmosphere and is a crucial part of water and many other compounds.

* Silicon (Si): Found in rocks, sand, and glass, silicon is the second most abundant element in the Earth's crust.

Compounds:

* Water (H₂O): The most abundant compound on Earth, essential for life and covering over 70% of the planet's surface.

* Quartz (SiO₂): A very common mineral, composed of silicon and oxygen, found in many types of rocks.

Therefore, the two most common elements are oxygen and silicon, and the two most common compounds are water and quartz.

It's important to note that "common" can be interpreted in different ways:

* By mass: The Earth's core is mostly iron, making it the most abundant element by mass.

* By volume: Water is the most abundant compound by volume on Earth's surface.

* By occurrence: Oxygen and silicon are the most common elements in the Earth's crust, which is where we primarily interact with them.