Answers
The shape of the atom depends on several factors, including the angular momentum of electrons and the electrostatic forces between atomic particles. It is not true that all atoms exhibit spherical shape; only the simplest of the atoms have that shape. Heavy atoms have more complex shapes.
Isolated atoms are spherically symmetric.
The s-orbitals are spherically symmetric.
Probabilty contour plots
Likewise, the sum of the probabililty functions of each subshell of orbitals (such as all three 2p orbitals, all five 3d orbitals, etc.) is also spherically symmetric.
For the above reason it is apparent that atoms with filled or half filled valence shells will have spherical symmetry, but what about the remaining atoms?
In 1965, Journal of Chemical Eduction published an article hapes of Atomsvolume 42 page 145, stating that atoms with filled or half filled valence shells are spherical, while the remainder are other shapes. A few months later a correction was published at volume 42 page 397, explaining that the original article failed to consider the fact that a valence electron in a isolated atom does not occupy a particular orbital; instead the wave function of the electon is a hybrid stateof all the orbitals of the valence subshell because they are degenerate.
See also Ruslan's comments below regarding the second J. Chem. Ed. article, that the proper description would be: the atom is in a mixed state.