Why planets look round?

The reason planets appear spherical is because gravity compresses the planet into a shape that most evenly distributes the gravitational force among the planet’s mass.
Whether it is shaping water droplets, stars, soap bubbles or planets, nature seeks to minimize the surface area needed to contain a given volume, and the shape that keeps volume at the absolute minimum a sphere.
Any object in weightless space larger than a couple of hundred miles in diameter has enough mass for its gravity to overcome large-scale irregularities and force it into a spherical shape.  This gravitational compression also generates significant amounts of heat at the center of the planet. This heat melts, or at least softens, any solid materials within the planet, facilitating the planet’s collapse into a spherical shape.
Objects in space smaller than about 100 miles in diameter, such as most asteroids, comet nuclei and small moons, lack the mass to create a gravitational field strong enough to compress themselves into spheres.  These little worlds often take on what I call the “sick potato” look