How can there be a God if he does not answer my prayers?
Prayer is a very deep subject believe it or not, there are many things about prayer that most Christians do not understand, or things that they have been confused about.  So before I answer the question about God answering prayers I think that it is appropriate to look at what prayer is all about, why we even should be praying in the first place, that might clear up a bit of this question, then we will talk about God answering prayers.
Four Parts to Prayer
It is best for us to break down prayer into four differen portions, so that we can better understand prayer.  Adoration, thanksgiving, repentence, and finally petition.  We'll take a look at each portion individually.
Adoration
The first and most important part of prayer.  Telling God just how awesome he is, and just how much what he does in our lives means to you.
Thanksgiving
Right along with telling God how much what he has done means to you and how awesome He is, is thanking Him for everything that he had done for you, your family, and everyone in the whole world.  Thank him for what he is doing, what he has done, and even what he will do.
Repentance
Face it, you are a sinner, I am a sinner, your pastor is a sinner, your neighbor is a sinner, even Pope John Paul II is a sinner.  The best part is, God is willing to wipe the slate clean, all you have to do is ask.  Once you have accepted Christ as your savior, it does not matter how many times you commit the same sin, God is willing to forgive you, all you have to do is ask.
Petition
This seems to be the area that everyone thinks is the entire reason for praying, asking God to do things for us.  Well, asking God for things is just a very small portion of praying.  Is God willing to help you out, if you ask, of course, but He isn't about to do everything for you, He also will not grant you every wish that you have, especially if he knows that it will bring you harm down the road, or lead you away from him.
God Answering Prayers
God, being all-knowing like he is, is willing to answer prayers.  Will he answer all of our prayers, yes.  Will  His answer to all of our prayers be yes? No.  Some may question whether he is really all-loving if he will refuse to answer some prayers with a yes.  Well, look at it this way, God knows much better than we do what will help us out the most in life.

Think really quickly about a life where God is to answer all the prayers with an "okay, whatever you want," everytime we ask.  It would look a bit like a sceen out of Bruce Almighty, we would all become so spoiled, that we would destroy ourselves.  In not answering all of our prayers with a "Okay, if its what you want, thats what you get" what God is really doing is looking out for our futures like only He can.