solar system - Why are planets round?

Gravity makes objects compress to their centers of mass, since gravity extends in all directions.

For planets, gravity continues compressing the object until the rocks cannot be compressed anymore, since the pressure will fight against gravity. At this point (called hydrostatic equilibrium), the object has become a spheroid. One of the requirements for an object to be called a "planet" is that it has reached hydrostatic equilibrium.

For black holes, the shape of their event horizons really depend on whether the black hole is spinning or not. For non-spinning black holes, gravity extends in all directions, so the event horizon will become spherical in shape. For spinning black holes, it will likely be an oblate spheroid.

Most galaxies are only spherical when they are forming. Their angular momentum usually causes them to flatten out over time. However, one part of galaxies, called the "halo", is spherical.

Wormholes are purely hypothetical, so I won't really entertain that.