(This is an entry for Weekend Fisher's Christian Reconciliation Carnival.)
A common misconception about Catholics is that we worship Mary, saints, statues, pictures, crucifixes, etc., and that in doing so, we're neglecting worship of God. (I dare say people think this is the "Roman" part of Roman Catholicism -- believing in some supernatural pantheon of gods and goddesses to whom we pray.) I'd like to briefly set the record straight on this topic.
The Catholic practice of veneration is showing devotion and respect to Mary, the Apostles, martyrs, and other saints who are clear examples of faithful witness to Jesus Christ. This respect extends to icons and other representations. Veneration is not the same as adoration and worship, which is given to God and God alone.
Veneration is not praising the person, it is praising what God made of that person, for we know that God is the source of all goodness, all virtue, all love. Veneration, then, points to God as the source of grace. The love Mary had for Jesus was not hers because Mary was "lucky", but because God chose her to be the mother of our Savior, and endowed her with the necessary grace to love him and stay by his side even to his crucifixion (John 19:25). Mary, then, is a model of the love God desires of us, just as Paul writes of himself as a model in his letter to the Philippians (Phil. 3:17). Catholics recognize as models for Christian living those who persevered in faith to the end (Matt. 10:22).
Similarly, Catholics don't pray to Mary or the saints, but ask them to intercede for us, just as we ask one another to intercede for us. We pray to God only, whether it be to Him as our Father, as our Lord and Savior Jesus Christ, or as the Holy Spirit. (Some explain it thus: we pray with Jesus, through the Holy Spirit, to the Father.) We don't ask saints to intercede for us instead of praying to God ourselves, just as we don't ask other people to pray for us without taking the time to pray ourselves. Let us not forget Mary's words to the servants at the wedding feast in Cana: "Do whatever he tells you." (John 2:5) This command reminds us of the source of our spiritual guidance and the recipient of our petitions and praise.