Well, for the most part they are in fact *colorless* and not white; colorless as in they do not absorb light and are thus transparent. However, their irregular surface in crystalline form can scatter light which appears white to us.
The reason they do not have a color is because they do not absorb light. Light is absorbed when the energy of a photon causes an electron to bump up to a higher orbital. This just requires too much energy in the case of most organic compounds, because they are small and their electrons are really happy where they are.
In larger compounds with lots of conjugation, the energy required to bump electrons up is much lower, resulting in the compound having a color.