Assortative mating is a term describing non random mating in which desirable characteristics are selected in a mate (www.anthro.palomar.edu). This is most common in humans, but exists in other species as well. Assortative mating is also thought to play a key role in speciation (Yuexin, J.).
Assortative mating is most common in humans, however there are examples of this selective mating in other species as well. For example the american robin is known to select its mate based on the color of its plumage.
http://anthro.palomar.edu/synthetic/synth_8.htm Assortative Mating in Animals. Yuexin Jiang, Daniel I. Bolnick, and Mark KirkpatrickThe American Naturalist , Vol. 181, No. 6 (June 2013), pp. E125-E138