Most sounds we perceive are transmitted through Air, the medium in which we normally live. These are produced whenever vibrations are excited in the air. Because these require motion, it makes sense that most sounds in Nature are due to the more dynamical aspects of it: Life, Fluids
See Ethology for the immense variety sounds that Animals produce.
Fluids include Liquids and Gases. The most prominent liquid is water, and indeed the interaction of water with gases (Bubbles), itself (waterfall, waves on the sea), or with Solid matter (Rain falling on the ground, or leaves, Pebbles rolling in a stream, etc.) are among the most common non-biological natural sounds.
The complex interaction with air with solid surfaces can also produce the recognizable sounds of Wind, sometimes producing sounds with a relatively clear pitch, like of air flowing through imperfect organ pipes.
Electrical phenomena, such as thunder, produce remarkable sounds where the air is directly stimulated by its sudden ionization.
Rocks falling downhill, volcanic eruptions, earthquakes, etc.