"Truly, truly, I say to you,
whatever you ask of the Father in my name, He will give it to you."
There are some interesting insights from some of the ancient teachers of the church concerning this, however. Origen points out that prior to Jesus, all prayers were directed solely to the Father. For a Jew to pray in anyone else's direction or name was considered idolatry. By praying to the Father in Jesus' name, we are implicitly acknowledging the lordship of Jesus and testifying to the truth he spoke, "No one comes to the Father except by me." (John 14:6) This is the proper way for a Christian to pray -- to the Father through the Father's designated mediator, our Lord Jesus. No other way is open.
Many of the church fathers and other teachers also point out that a good and loving Father does not give everything his children ask for. Sometimes (often times) children have no idea what is in their best interests to receive, so a loving father will say no to requests which may harm a child or are just not the best way forward. Many prayers fall into this category when we stop to think about them, or once we gain deeper insight and maturity.
Another ancient church father, Bede, wrote clearly on the notion that the Father and his Son always have eternal salvation in mind for their creatures. So any prayer that fails to move one towards a strengthened faith and closer to salvation is immediately suspect, and may not be appropriate for us from the Father's viewpoint.
Lastly, we should remember that in the Garden of Gethsemane Jesus himself prayed to his Father for the cup to be lifted from him, but closed his prayer with "Thy will be done." This is a good reminder that we place ourselves into the hands of the Lord and trust him to act in our best interests even if it means getting a "no" to one of our prayers. Like any father, our heavenly Father loves being peppered with questions and requests from His children. He undoubtedly delights in giving all good things to us, and probably even chuckles over the things we ask for that He knows He needs to say no to. After all, Psalm 2:4 reminds us, "He who sits in the heavens laughs."
So pray your prayers with a joyful spirit through Jesus, sure in the confidence that our Father in heaven has heard them and will act according to His good and gracious will, which, of course, is far more reliable than our own wishes and desires.