In ancient times baubles and trinkets were given by men to their finacees as symbols of status. In many books of prayer surrounding weddings (http://en.wikipedia.org/wiki/Wedding_ring) a ring is referenced.

The practice of giving rings had fallen out of favor in modern times until the de Beers diamond company came up with an ad campaign which is one of the most effective in history as it basically cemented the practice of engagement/wedding rings, said how much they were supposed to cost (two months salary!) and made the concept so ubiquitous that it's almost unheard of not to present rings.