The Catholic Church teaches that worship is reserved for God alone. While Mary is not worshipped, she is given the honor proper to her as the Mother of our Lord Jesus and as a faithful servant of God (Luke 1:43, 45).
The Catholic Church makes a distinction between three types of veneration: latria (the worship due to God alone), dulia (the honor appropriate for the angels and saints in heaven) and hyperdulia (the special honor appropriate for the Blessed Virgin Mary). The difference between latria and dulia is not a difference in degree but in kind: “dulia and latria [are] as far apart as are the creature and the Creator.” (Pace)
The Second Vatican Council clearly taught that “no creature could ever be counted as equal with the Incarnate Word and Redeemer” (LG, 62); this affirmation holds true in the case of the Mother of God: “The Church does not hesitate to profess this subordinate role of Mary” (LG, 62).
While the Council asked that an appropriate veneration of Mary “be generously fostered” among the faithful, it also warned against excesses: “[This council] exhorts theologians and preachers of the divine word to abstain zealously both from all gross exaggerations as well as from petty narrow-mindedness in considering the singular dignity of the Mother of God. Following the study of Sacred Scripture, the Holy Fathers, the doctors and liturgy of the Church, and under the guidance of the Church's magisterium, let them rightly illustrate the duties and privileges of the Blessed Virgin which always look to Christ, the source of all truth, sanctity and piety. Let them assiduously keep away from whatever, either by word or deed, could lead separated brethren or any other into error regarding the true doctrine of the Church” (LG, 67).
Thus, the Catholic Church does not encourage the faithful to worship Mary. Any possible excesses among the faithful are contrary to the explicit teaching of the Church and do not represent correct Catholic practice (any more than, e.g., a few evangelical Protestants hero-worshiping a popular preacher is representative of authentic evangelical Protestant beliefs and practices).
Many Protestants, wary of excesses in Marian devotion, tend to ignore Mary altogether. The Catholic Church, on the other hand, follows Scripture in giving special honor to Mary. One example is found in Luke 1.28, 30: “The angel went to [Mary] and said, ‘Greetings, you who are highly favored! The Lord is with you.’ […] But the angel said to her, ‘Do not be afraid, Mary; you have found favor with God.’”
Another example is in Luke 1:41-45: “When Elizabeth heard Mary’s greeting, the baby leaped in her womb, and Elizabeth was filled with the Holy Spirit. In a loud voice she exclaimed: ‘Blessed are you among women, and blessed is the child you will bear! But why am I so favored, that the mother of my Lord should come to me? As soon as the sound of your greeting reached my ears, the baby in my womb leaped for joy. Blessed is she who has believed that the Lord would fulfill his promises to her!’”
Filled with the Holy Spirit, Elizabeth commends Mary as being blessed among women; she is honored to be in Mary’s presence by the very fact that Mary is the mother of our Lord Jesus. Neither the archangel Gabriel nor Elizabeth (whom Scripture says was “filled with the Holy Spirit”) are engaging in sinful, excessive honor of Mary that obscures the worship due to God alone. Instead, both instances demonstrate that such honor is appropriate, and in no way does it diminishes one’s exclusive worship of God.
These two passages form the basis for the first part of the most common form of Marian devotion – the “Hail Mary” prayer. The first line of the prayer, ‘Hail, Mary, full of grace, the Lord is with thee’, is simply an older translation of the angel Gabriel’s greeting to Mary. And the prayer’s next line, ‘Blessed art thou among women, and blessed is the fruit of thy womb Jesus’, is taken from Elizabeth’s greeting to Mary.
Catholics are also following the example of Jesus in honoring Mary. In his work, True Devotion to the Blessed Virgin, the 18th century spiritual writer, St. Louis de Montfort, pointed out that Jesus, being sinless, would have obeyed the fourth commandment to “[h]onor your father and your mother,” and so we become imitators of Jesus himself in giving appropriate honor to Mary. (TDBV, 139-14)
Some claim that Luke 11:27-28 is an example of Jesus dismissing honor given to Mary: “[A] woman in the crowd raised her voice and said to him, ‘Blessed is the womb that bore you, and the breasts at which you nursed!’ But he said, ‘Blessed rather are those who hear the word of God and keep it!’” However, we already know from the passages already quoted that giving special honor to Mary is appropriate. Rather, Jesus is highlighting the fact that Mary’s faith is of greater importance than her role as the physical mother of Jesus, as important as that role is (Luke 1;43); this corresponds with the latter part of Elizabeth’s praise of Mary: “Blessed is she who has believed that the Lord would fulfill his promises to her!” (Luke 1:45).
Pace, Edward. "Dulia." The Catholic Encyclopedia. Vol. 5. New York: Robert Appleton Company, 1909. 27 Nov. 2012 .
Scripture quotations are taken from the New International Version (NIV)