The other planets are very clearly spherical. Not a single one is a flat disc.
Roughly spherical. Jupiter spins so quickly (< 10 hr) that it is visibly flattened in a telescope. Just like the earth, only more so, demonstrating that the earth is just another planet following the same physical laws. It doesn't matter whether the object is solid, liquid, gas or plasma, if it's massive enough to have significant gravity, it will approximately attain the shape (an oblate spheroid) with a constant surface gravitational potential energy. (Note,
not constant surface gravitational acceleration; that's the derivative of the potential function with respect to radius, i.e., how quickly the potential energy increases with altitude.) The exact shape of the earth's equipotential surface is called the
geoid. It is approximately equal to sea level.
The earth is still well approximated by an oblate spheroid; its equatorial radius is about 22 km greater than its polar radius (Mt. Everest is only 8.8 km above sea level). The geoid deviates only about +/- 100 meters from this, mainly due to a non-homogeneous interior. But those deviations are still very important to those living on coastlines.
Bodies that turn more slowly are much closer to being perfectly spherical, e.g., Sol (our sun), Mercury, Venus and Luna (our moon).