A good, straightforward question - I like it. They’re round because they’re huge!

Basically the spherical shape of planets and stars comes from the fact that they contain so much mass that they have reasonably sized gravitational fields. The mass in any object pulls other masses in toward it. Just as you and I feel the pull of the Earth downward so does the Earth itself.

So every point on the Earth (or any other planet) pulls on every other point. This results in a sphere since it is the only shape where all the gravity forces are balanced throughout the body.

Smaller objects like some of the asteroids and Mars’ moon’s Phobos and Deimos are not spherical. They are not big enough and do not contain enough mass for the gravity to be more powerful than the rock’s internal structure - known as rigid body forces. This condition, that an object can overcome these rigid forces and be spherical, is one of the parameters that the IAU used recently to determine what is a planet and what is not. Spherical objects are planets (or dwarf planets) and non-spherical ones are not.

This is also why we not have 100 mile high mountains on the Earth. If we did then they would collapse under their own gravity.

Some forces can overcome this spherical shape however. The spin of the Earth on its axis is fast enough that the resulting centrifugal force creates a bulge around the equator, making the Earth a little fat. In facts its about 25 miles wider at its middle than at its top.

In Jupiter, the planet is larger and made of less rigid material (i.e. liquid gases) and so the bulge in its middle is pronounced enough to see in pictures like the one above.