Question

why are the planets round

Answer 1

Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment." 

With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes.

Answer 2

Planets are round because during his early age of planets, it's surface and interior are hot and liquid form as it is forming, just as gaseous planets, the gravity acts as balance force and make surface round towards core due to gravity as same as gaseous planets and in course of time the hot surface cools and solidified as we see.
Stars are round also by this way