What exactly is worship? Why do we worship and what is actually going on when we worship? For Christians (Catholics, Eastern Orthodoxy, Protestants), we worship only one being, the supernatural being we call "God". We worship God because we believe He created us. We believed He not only created us, but He also created everything else you see in the natural world; all the plants, animals, chemicals & metals, planets & stars, and another kind of being we call Angels (more about them will be said later on). Such a powerful being must not have any bad in him and he cannot mix up with bad things. But we have become bad out of our own will and weakness. As a result, our souls cannot be with God because our souls are not pure. However, God is Love; He has infinite Mercy. He still wants to be with us and us to be with Him. So He made a deal with us (ie: a Covenant). He said that He will send His Son down to us. His Son will suffer and die in order to wash away our sins. In other words, He died so that we might live. If we believe all that (and admit, of course, that we have upsetted him), then we have a chance to be with God; we are qualified to be part of God's family and be able to live in the Glory of God the Father (AMEN). That is why we worship God. It is because, besides being our Creator, He is our Savior. He is our Father. So we give Him our highest level of respect; we worship him.
When we worship, we are giving God more respect than we would of anything else. We want to establish a relationship with God to as high a degree as possible by whatever means. There are many ways we can worship and praise; songs, prayers, signs & symbols, and rituals are all different means by which Christians do their worship. Even just simply obeying the rules and showing a love for one another are things that we can do to glorify God. In worshipping, we are humbling ourselves and submitting ourselves to doing what pleases God. We recognize that He is there and He will bestown gifts (ie: Grace) to those who please Him. We gladly accept these gifts because they give us spiritual strength and enrichment and we are thereby drawn ever closer to God.
For Christians, that can be done because of God's only Son, Jesus Christ. It was because of Christ that we have a chance to be with God. It is because of our Big Brother who stood out for us that we can believe and so qualify for the race where the prize is eternal life in His Glory. That is why Jesus Christ is the "only one Mediator between God and men." But does that mean God can only be accessed by means of Christ? Ultimately, yes. We need Christ in order to be placed in the path that will lead to eternal life. However, because of our obligation to practice love for one another as Christians, people who don't know God can come to know God through us. This doesn't mean that the ones who have not believed can be redeemed because of us. It just means that we, who are all members of God's family, are in the same spiritual life-and-death situation; we can help each other get through as we struggle to battle the forces that attempt to keep us off our path to eternal life.
When we consider the members of God's family, we must not limit them to just the humans on this earth who are physically alive. We are not to forget that those who have come before us as well as the Good Angels are also members of the Family. They are constantly praying for us and making intercessions. It would not make sense if they are alive enough to pray for us and yet not alive enough to know anything that is actually happening on earth. Therefore, there should be nothing wrong with praying to them. What we are really doing when we pray to them is that we are simply talking to them. We are saying, "N, I am having trouble here. But I know that you are enjoying yourself up there and I am happy for that. So won't you please help me out here and pray for me?" While we are not to get direct responses from them, those in heaven nevertheless know our situation and will make intercessions for us. Most of us, most of the time, are not qualified to witness heavenly beings. They are perfect, we are not.
I think it may be the human being's natural tendency to feel that a dead person is not really totally dead - just the body but not the spirit. Consider the situation for Princess Diana's funeral service. People from all around the globe were sending her cards, teddy bears, and flowers. But the lady is dead! And yet we see the entire street lined with flowers and stuff for blocks! Now, is this wrong? Is this not communicating with the dead? But are we worshipping her? Of course we're not. Neither are we when we pray to Saints.
Perhaps something else to consider may be on different levels of worship. Protestants consider prayer and song to be worship. They also think that kneeling in front of something and talking to it is in fact worshipping it. Catholics, on the other hand, don't consider that as necessarily worship. Catholics do kneel down, pray, and sing songs to worship God. But the key difference is that we worship in an even higher level than Protestants. We have bread changed into the Body of Christ so that we can consume it and have everlasting life - because we are eating "the Bread of Life". This is our highest form of worship; something that Protestants lack.
Finally, you should consider what "worship" really means to you. Do you think that kneeling in front of statues and praying to it is worshipping it or the person whom the statue represents? You probably have to decide that for yourself. I personally think that if you feel in your heart that you not worshipping Mary when you pray to her, then you probably aren't. So then who cares what people perceive you to be doing?
Have a look at this page which contains links to various other sites related to Catholic Worship.