Apparently some non-Catholic readers were scandalized by my reference to praying to the saints, so I wanted to explain and clarify things.
Catholics believe in a concept, articulated in the Nicene Creed which has been the standard of the Christian faith since 325 A.D. (it came from the council that first defended Christ's divinity), called the Communion of Saints. The Communion of Saints says that there is a kind of unity or bond among all believers. "Fellowship" is the way some translations of Scripture express the concept.
One of the concepts behind the Communion of Saints is that the saints who have gone before us are around us and can hear our prayers. This is demonstrated by Hebrews 12:1 (which says we are surrounded by the saints who have gone before), Hebrews 12:23 (which says the saints are present when we worship), and Revelation 5:8, the elders in heaven carry the prayers of the saints (incense) to the throne room of God.
Even if we did not know from the testimony of Scripture that the saints are around us and carry our prayers to the throne room of God, it would make sense that we could ask for their prayers and they could intercede for us. When my mother died, I wanted very much to talk to her. I reasoned that I could pray to God and ask him to give her a message for me. He could then do so if He so willed. Then I said that I'll just talk to her and intend the same thing; i.e., instead of praying, "God, could you please tell my mom I love you," just tell God that when I say, "Mom, I love you", I mean "God, could you please ..." etc.
This is how I came to accept the communion of the saints.
Now, about the concept of "praying to" saints.
First of all, it should be noted that while "pray" has a connotion of worship in some uses in English, it is not so in Latin. In Latin, the word for "pray" is the same word as "ask". So, in Latin, to "pray to" a saint is synonymous with "asking" a saint. Praying to saints has no connotion of worship. Catholicism strictly forbids worshipping saints (in the sense the term currently has in English). Adoration belongs to God alone, and God alone is to be adored. When we pray to saints, we are merely asking them to pray for us as we'd ask a friend to pray for us. Protestants tend to assume that prayer=worship mostly because they do not pray to anyone they do not worship. This is not so for Catholics.
Which brings up the question, why ask saints to pray for us? Well, first of all, the "prayer of a righteous man is powerful and effective" (Jas 5:16). And the saints in heaven are more righteous than we are on earth because they have been perfected (Heb 12:23). Second of all, they have a role of interceding for us, as Jeremiah 15:1 demonstrates.
A lot of people object, "Well you can pray to God directly!" Well, yeah, you sure can, but funny how people who object to asking saints to pray for them have no qualms about asking members of their church to pray for them! It's the same concept. The more the merrier. Objecting that we can pray to God directly is a bit like saying "No thank you, I can hold all ten of these objects myself, I don't need any help." Sure, you can and should carry your own burden, but why carry it totally alone? Also it is good to have people more righteous than us praying for us as James 5:16 says. Ours is not an individualistic religion. We are interdependent people.
The other reason to do it is because it works — in fact it works miracles. Few people know that for the last millenium or so, in order for a saint to be canonized, two verifiable miracles have to be worked by their intercession. That's right: the church requires an actual miracle before someone can be beatified, and another before they can be canonized. I met the father of a girl (he's a Melkite Catholic priest) whose miraculous healing of a Tylenol overdose was the canonization miracle for Edith Stein. I mean, isn't Catholicism great? What other religion requires and expects miracles as a part of its fundamental operation?! This is also how we know that saints with vague historical documentation exist — because they still work miracles.
Another objection people have is "well how do they hear millions of prayers"? I could answer this silly question and say that perhaps the prayers get turned into some sort of force they feel or they perceive them in some non-verbal way, but I'm going to respond to it in a very simple and straightforward way: God became man in Jesus Christ. Jesus is still man; he did not lay aside his earthly body. The man you worship and pray to is a flesh and blood man about five foot eight or so with a brain like yours who is presently running the universe. If Jesus, who is man and will forever remain man, can hear your prayers, what makes you think other men cannot?
Another objection is that we are violating the commandment against contact with the dead by praying to the saints. No, because it is a one-way request. There is no communication as if we were receiving answers back; how can a one-way request be dangerous? The whole arguing against divination pertains to the danger it poses if you follow the messages you receive that way. If you aren't receiving messages, the issue is moot.
So when we say we "pray to" saints, we are not worshipping them, but asking them to pray for us, which we can do because they are all around us (Hebrews 12) and have a role of carrying our prayers to the throneroom of God (Rev 5) and interceding for us (Jer 15:1).
Here are some additional verses from the Catholic bible (which are not found in Protestant bibles). I offer them only as evidence that this concept was not invented in the Middle Ages.
Baruch 3:40: "Lord Almighty, God of Israel, hear now the prayer of the
dead of Israel and of the sons of those who sinned before Thee, who
did not heed the voice of the Lord their God, so that calamities have
clung to us."
"Thus he armed every one of them, not so much with defence of shields
and spears, as with comfortable and good words: and beside that, he
told them a dream worthy to be believed, as if it had been so indeed,
which did not a little rejoice them. And this was his vision: That
Onias, who had been high priest, a virtuous and a good man, reverend
in conversation, gentle in condition, well spoken also, and exercised
from a child in all points of virtue, holding up his hands prayed for
the whole body of the Jews. This done, in like manner there appeared a
man with gray hairs, and exceeding glorious, who was of a wonderful
and excellent majesty. Then Onias answered, saying, This is a lover of
the brethren, who prayeth much for the people, and for the holy city,
to wit, Jeremias the prophet of God. Whereupon Jeremias holding forth
his right hand gave to Judas a sword of gold, and in giving it spake
thus, Take this holy sword, a gift from God, with the which thou shalt
wound the adversaries." (2Mac 15:11-16 KJV)

I've asked many a saint for his or her prayers.
And I can say they do work. My Jewish boss alway asks me to pray to St. Anthony when she loses something. Most people who initially think praying to saints is blasphemy, come around when I explain that it's exactly the same as me asking them to pray for me.
I have no doubt that the yet-to-be-resurrected saints in the heavenly realms do pray for the church militant, but I don't think they receive and hear the prayers of the church militant nor that their petitions have greater gravity than those of living saints.
All saints of God, living (us) and dead (those who are asleep in Christ, waiting the resurrection) are equally meritless of God's favor yet equally immersed in the infinite riches of God's grace to approach the throne of grace. Only Christ alone stands before the throne of God continually in His resurrected, glorified body, continually interceding for the saints. Possessing eternally the omniscence and omnipotent of God, he hears the prayers of all the saints and there is no need for saintly intercession, particularly since it leads to a spiritual idolatry upon which living saints lean upon those who departed in Christ for the grace and favor of God, rather than directly going to the Father through His Son Jesus Christ.
Additionally, I see no precedent in the old covenant for saintly intercession. David did not pray to Abraham, Isaac, and Jacob, he prayed directly to God, even though he in his time lacked the revelation of the Messiah, only possessing the notion of the future unveiling of the Messiah to atone for his sins.
So if David, having not Christ, can appeal directly to God's graces, how much more so shall we only approach God directly through the gift of His Son, our Messiah, Jesus Christ, whom God pleasured to have revealed upon the earth prior to our lifetime so that we would ever know the revealed image of God.
Anyway, just my thoughts on the matter.