A part of DNA molecule, on a black background
An ammonite fossil. Some other sea life forms also have a spiral shape.
Stirring in a vortex-like fashion is the most common way of mixing 2 or more ingredients, or components (e.g. cement and water).
This is a maelstream, a powerful currrent off the coast of Norway. "Maelstream" has also been the image of the state of confusion, e.g. international affairs.
The shape of clouds, for example after a cyclone
Most galaxies, like this NGC 4414, have a spiral shape.
Inside Guggenheim Art Museum in New York. Spiral shape of ascent or descent.
Humanity is said to develop in a spiral fashion. This is a drawing for the monument to the Communist International, designed by Tatlin in 1919. Original description of the project is here: http://tehne.com/event/koncepty/pamyatnik-iii-internacionala-proekt-v-e-tatlina-1920