Why are skin moles (pigmented spots) circular in shape?
Note: I am not stating that moles are in general circular in shape because there are no statistical studies to conclusively state so. This answer is mostly about default circular shape of cell colonies.



Moles (melanocytic naevi) are not strictly circular but generally have  have a rough circular shape. Moles can have irregular shapes too and you can easily check that by a simple google image search. 

The exact causes and mechanisms of mole formation are not known but the somewhat circular shape can be explained by a simple spatiotemporal model of growth. 

Moles are formed because of pigmented cells called melanocytes (which contain the dark pigment melanin). A mole would grow when a very small population of these pigmented cells divide and expand. In a 2D surface, cells would continue to divide and expand along both the axis at an equal rate, if there are no specific constraints. Since the expansion is same along both the axes, you get a roughly circular shape. For similar reasons, bacterial colonies (on petri plates) are also more or less circular. Note that there are stochastic factors that would contribute to irregularity.

Triangles and rectangles are very specific geometries. There need to be some constraints that would limit the cell growth to adopt these geometries. So the default shape would be mostly circular.