According to the Western tradition (and the Eastern tradition?) today is the day that we celebrate Mary, the mother of God. When I was younger I remember being told that this title was inappropriate because it somehow suggested the eternality or deity of Mary. It was emphasized that Mary was the mother of the humanity of Jesus. It was not until I was in college that I learned that this was a subject debated in the early church.
The defenders of the term Theotokos (Gk = one who gives birth to God [Θεοτόκος]) debated those who argued that the term Christotokos (Gk = one who gives birth to Christ) was more appropriate because God is eternal and God cannot be born. Against the defenders of Christotokos it is argued,
Since Mary is Jesus’ mother, it must be concluded that she is also the Mother of God: If Mary is the mother of Jesus, and if Jesus is God, then Mary is the Mother of God. There is no way out of this logical syllogism, the valid form of which has been recognized by classical logicians since before the time of Christ. 
Adrian Fortescue wrote,
It follows obviously from the hypostatic union: she is the mother of Christ, the mother of a person, and that person is God. The relation of mother and son concerns persons. The mother of a person who is God is just as much Mother of God as the mother of a person who is man is mother of man. 
Those who were in error–the Christotokos–were mistaken in their understanding of Christ. Most at the time of the controversy were of the party of Nestorius who said Christ was two persons.  Orthodoxy maintains that Christ is one person with two natures. Therefore, we cannot speak of Christ as being human on one end and God on another. Since Christ is God it is understood that Mary is the mother of God who was born in the incarnation.
It needs to be understood by those who reacts negatively to this title that it does not suggest the eternality of Mary nor does it suggest that the eternal God is temporal. Mary, the mother of God, suggest that the incarnation was a real occurrence in our history in our world. We confess that the man Jesus of Nazareth was the creator God.
 “Mary, Mother of God” accessed from http://www.catholic.com/library/Mary_Mother_of_God.asp on 1 January 2010.
 Adrian Fortescue, The Greek Fathers: Their Lives and Writings, San Francisco, CA: Ignatius Press, 2007 (reprint from 1908). 171-172.
 Ibid. 170.