Why do liquids assume a spherical shape when in zero gravity?

Actually, not only in zero gravity the liquids acquire a spherical shape. Differential density and molecular affinity also play an important role in the formation of spheres. This is one of molecular gastronomy's favourite tricks and they calle it spherification.

The sphere (or ball) is a very economical shape. Any other shape would have a larger surface for the same volume. Accodring to wikipedia The sphere has the smallest surface area among all surfaces enclosing a given volume and it encloses the largest volume among all closed surfaces with a given surface area.

For this reason, the sphere appears in nature: for instance bubbles and small water drops are roughly spherical, because the surface tension locally minimizes surface area.

It's caused by cohesion/surface tension. The molecules of the liquid all pull each other towards themselves, which makes it try to achieve the smallest possible surface area for the given volume, and the sphere has the smallest surface area to volume ratio. You can see the effects of this in normal gravity too.

Water drops try to achieve the most spherical shape they can, but gravity pulls them down.

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