There are way too many to list. Everything in science is inspired by a natural phenomenon of some kind, if you trace its history. The list would include thousands or hundreds of thousands of items.

• Amber attracts small pieces of paper. This led to the study of static electricity. The properties of natural magnetic rocks led to the study of magnetism.
• That smoke rises and moves wildly was one of the properties of small objects that led Democritus to propose atomic theory. The theory of Brownian motion came much later. The phenomenon of freezing, melting, boiling, at certain very sharply defined temperatures was also important, and the theory of phase transitions in large statistical systems also came much later.
• You can see farther higher up. This led the ancient Greeks to understand that the Earth is a sphere.
• The phenomena of "days" and "nights" and everything in the sky moving together, led Aristarchus and others to propose that the spherical Earth rotates.
• The retrograde planetary motion (and the fact that the sun is bigger than the Earth) led Aristarchus to propose that the earth moves around the sun.
• There are no-shadows on the equator at equinox at noon. This allowed Aristarchus to get an estimate of the diameter of the Earth.
• Things can float in water. This led Archimedes to the concept of bouyancy force, and accurate density measurements.
• Any object can be made to balance on another. This led Archimedes to formulate the concept of center of mass
• The observation that thrown objects fly without a propelling force led to the theory of inertia.
• Blood circulation. This wouldn't have been so monumental, except that Aristotle, among his many idiocies, said that blood goes back and forth.
• The observation that magnets attract and repel at a distance according to a definite inverse-cube law gave rise to the Newtonian era conception of forces acting on objects at a distance.
• The moon is roughly the same brightness at all points. This means that it reflects light equally in all directions, which implies that it is rough not smooth. This argument is by Galileo.
• Big animals are chunky, small animals are lean. Big sticks break more easily than small sticks. This led Galileo to note that there is a fundamental length scale to matter in "Two New sciences".
• Echoes give the speed of sound
• The observation that objects exchange heat until they come to the same temperature, and that heat never goes from a hotter to a colder body, gave rise to the science of thermodynamics.
• Rainstorm lightning inspired artificial static electricity devices which generate large voltages and sparks, like the Van de Graaff generator and the Kelvin thunderstorm.
• Water at a certain high pressure and temperature becomes milky white. This critical opalescence inspired the scientific theory of second-order phase transitions. This theory gives a definition of statistical fields, and is fundamental to modern mathematical physics.
• The roughness of natural boundaries like coastlines inspired Mandelbrot's theory of fractals, which gave mathematical quantities which describe the properties of rough shapes.
• The observation that objects exchange heat until they come to the same temperature, and that heat never goes from a hotter to a colder body, gave rise to the science of thermodynamics.
• The observation that magnets attract and repel at a distance gave rise to the Newtonian conception of forces acting on objects at a distance.
• The observation that a magnet passing by a loop of wire gives rise to a current the same current as a loop of wire passing by a magnet, gave rise to Einstein's theory of relativity.
• The sun and stars inspired the analysis of nuclear fusion.
• Bird flight inspired fixed-wing flight, it was clear that it was possible from the fact that birds can glide with wings fixed.
• The natural phenomenon of thinking in brains, humans doing mathematics, was abstracted to computational devices by Alan Turing in 1936.
• Bacterial replication inspired Von-Neumann's biological interpretation of Godel's theorem--- in the theory of self-replicating automata.
• Biological self regulation was the basis of the early computational ideas of cybernetics.
• Heredity led to genetic theory.

The list is ridiculous, I went on, then stopped arbitrarily because if you take any natural phenomenon and look at how the science of it developed, you get a story like this.