Well, to be true, it does not fall so neatly along Protestant/Catholic lines (which fully neglect Orthodox and Evangelical Christianity), but that is immaterial to the discussion.
Works: The book of James is often the best support for works based salvation. The oft-quoted passage comes from James 2:18-19.
18But someone will say, "You have faith; I have deeds."
Show me your faith without deeds, and I will show you my faith by what I do.
19You believe that there is one God. Good! Even the demons believe that—and shudder.
This is basically saying that just believing that there is a God is enough, because those damned to hell believe in Him. Rather, you must prove that this belief in some way affects you, because if you truly believed then you would desire to do good things.
Faith: The concept that all have sinned and none are worthy of being in Heaven, as well as the demands to be "more righteous than the Pharisees" in order to enter heaven, lend credence to the idea that salvation is only a matter of faith.
Romans 11:16 says, "And if by grace, then it is no longer by works; if it were, grace would no longer be grace."
There are hundreds of passages that talk about belief and how belief is fundamental to a relationship with the Father.
Synthesis: Both are necessary for salvation. Without faith, what good are works? If you only do things because you are supposed to, not because you believe they are right or with a belief in the truth of God, how is that supposed to please God? Does he only desire lip service? God desires your heart and soul more than your body. The body is temporary, but the spirit is eternal.
Without works, there is no evidence of faith. As the saying goes, talk is cheap. If you have no proof that you believe, do you really believe? A true belief will cause a change that makes you desire the things of God and to do the good works of God. We are also called to bring truth to others, and just speaking about God rarely convinces people. Showing that God has affected your life to a great degree is infinitely more effective than the words of an inactive believer.
To pick up on some questions I missed: Yes, there are some Protestant denominations that feel that there are certain deeds necessary to get into Heaven, but things like this vary from church to church, and from person to person.
From what I understand, someone who just believes is not really a Christian, so therefore no access to heaven. You don't become a Christian until you go through certain Catholic rites, such as baptism and the Eucharist.
I hope this helped some. I only included a few passages of scripture in my sources, but there are plenty more.
Matthew 25:31-46, 2 Timothy 2:19, James 2:14-26, Romans 4, Romans 11:16, various passages on grace, belief, deeds and salvation