The color for a coordination complex [2] can be predicted using the Crystal Field Theory (CFT) [3]. Knowing the color can have a number of useful applications, such as the creation of pigments for dyes in the textile industry. The tendency for coordination complexes to display such a wide array of colors is merely coincidental; their absorption energies happen to fall within range of the visible light spectrum.
Links
[1] https://www.hootsgo.org/?q=node/6460
[2] http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Coordination_Chemistry/Basics_of_Coordination_Chemistry/Introduction_to_Coordination_Chemistry
[3] http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Crystal_Field_Theory/Crystal_Field_Theory
[4] http://www.chemguide.co.uk/inorganic/complexions/colour.html