There is a more superficial argument that Catholics worship saints and Mary, however, this is not the case as they are only revered and respected, Catholics keep the focus on God only asking Mary and the Saints to pray for them. To worship Mary the same as one would worship Jesus or God or the Holy Spirit is expressly condemned by the Catechism.

971 (Worship of Mary) differs essentially from the adoration which is given to the incarnate Word and equally to the Father and the Holy Spirit

Catechism of the Catholic Church

2680 Prayer is primarily addressed to the Father; it can also be directed toward Jesus, particularly by the invocation of his holy name: “Lord Jesus Christ, Son of God, have mercy on us sinners.”

Catechism of the Catholic Church

The Catechism clearly states that prayers are addressed to the Father. If you are praying, God hears it, no matter what. If prayer is “secondarily addressed” to a specific saint, this does not mean that it is only heard by the saint and that the one who is praying thinks that the saint is the one that will help them.  

This is not necromancy, as so many Protestants believe, which is expressly condemned in the Bible and by the Catholic Church. Necromancy is contacting the dead in order to learn about the future. Jesus talked with the dead, Elijah (raptured) and Moses (dead) appeared and talked with Jesus in Luke 9:29-31, but this was permissible because it was not to learn more about the future.

Hebrews 12:1 seems to suggest that we are constantly surrounded by a “communion of witnesses.” This scripture lends itself to the Catholic position because whenever the New Testament refers to a “race” it is referring to humanity’s lifelong struggle against sin, both publicly and privately. Since we are surrounded by witnesses, who have already “run the race,” in our private lives, one can assume that this means a communion of saints.

This communion is part of the Body of Christ. Communal prayer is very useful for building up the Body of Christ, both in the temporal world and in the spiritual world. Catholics believe that by praying with the saints and with other believers still “running the race,” they not only build community with the earthly Body of Christ but the heavenly one as well.

Furthermore, if we can just go to God with our prayers, why do we ask each other to pray for us? Because it is useful for building community with other believers.

My friend Mr. Jones made a fantastic point about the intercession of Mary and saints; he said that if God hears everything and he hears you pray to a saint with the intention of Him hearing you, will He really refuse to hear/answer your prayer? I do not think so.

There is also some biblical support for the intercession of Mary and the saints. Revelations 5:8 describes 24 elders that are holding up the prayers of God’s people. This can be interpreted as a metaphor.

On the other side, Protestants claim that to say to claim that a saint can hear thousands, maybe even more prayers at one time is to make that saint out to be universal, a quality that is reserved only for God. God can speak to us through the testimony of the saints, but we can not speak to the saints.

Even if we could, why would we want to? We have a perfect savior who knows our hearts and what we need. Jesus Christ is the perfect mediator between God and man, and because Jesus is perfect, there is no need for anything else.

Analysis: Since Christ came as the sole mediator between man and God, we can pray directly to God the Father. Asking the saints or Mary to pray for something is not polytheism and it is not blasphemy, as long as it is done with the right heart. If someone prays with the saints to build up the whole community of believers, there could be a good heart behind this. If someone prays to the saints so that the saints themselves will offer protection or help, this is blasphemy.

It would be better to only pray to Jesus and to completely avoid praying to saints if there is even a doubt about it in your mind. It would be better to sacrifice community with other believers, which is what you gain by praying to the saints, than it would be to sacrifice the universality of Christ and true biblical doctrine.

Citations:

“Catechism of the Catholic Church.” Vatican, Libreria Editrice Vaticana, 1993, http://www.vatican.va/archive/ENG0015/_INDEX.HTM.
“Saint Worship?” Edited by Robert H. Brom, Trinitarian Baptism | Catholic Answers, Catholic Answers, http://www.catholic.com/tract/saint-worship.