"Catholics believe you need works to be saved." I've heard this argument time and again from well-meaning friends and a few authors. The truth is that Catholicism does not believe this either, since as Paul said in Ephesians, "For it is by grace you have been saved through faith, and this is not from you; it is the gift of God; it is not from works, so no one may boast." (Eph. 2:8-9) All Christians agree that God's grace is what ultimately saves us, His free, undeserving grace. But, Paul also wrote that we are to "work out [our] salvation through fear and trembling" (Philippians 2:12). What it boils down to are two different perspectives on another principle: justification.
To most Protestants, justification is like a court trial. We, as sinners, stand before God and are deemed innocent because Christ's blood covers our sins. Luther described this as a snow-covered pile of dung, clean on the outside, but not on the inside. This view is prevalent in many Protestant denominations.
Catholics view justification more in terms of bathing or healing, like someone washing another or a doctor tending to a sick patient to make him healthier. With this, there is a transformation that takes place. Now, I know there are many Protestants who would agree with this, yet still use the court trial analogy.
Another analogy would the story of the leper found in the Gospels. In Mark, Jesus cleanses a leper (Mark 2:40-45). Here, Jesus does not merely call the man clean, he transforms and heals him, even touching him (in Jewish law, touching something unclean also made you unclean)! This shows that Jesus is the source of cleanliness and transformation, purely clean so that no thing can make him unclean. Psalm 51 illustrates this as well. Here, David prays to God to blot out his offenses (more legal) (v.1), cleanse him (intrinsic) (v.2), wash him to be like snow (intrinsic) (v.7), and blot out iniquities (legal) (v.9).
This is where works comes in. While we are initially cleansed and justified, Catholics see another step: progressive justification, or sanctification. While the quality of the initial justification is perfect, our quantity is relatively small. Here's a recent analogy I came upon:
Say you have a glass of 100% pure water. That represents our righteousness. Jesus' righteousness is like an ocean, vast and infinite, while ours is quite finite. Sanctification is like adding more water to our glass (or getting a larger glass of water), and this addition comes through our good works within God's grace and with the help of His grace. In other words, doing a good work for selfish or wrong motives is not a purely good work.
The opposite is also true. Not doing purely good works diminishes our righteousness. James said it well when he wrote, "Faith of itself, if it does not have works, is dead" (2:17). He then talks of Abraham and Rahab and how they were rewarded for their works (2:21-25), and concludes with this: "For just as a body without spirit is dead, so also faith without works is dead" (2:26). A dead faith is no good to the Church or to God. It's like a runner just barely crossing the starting line of a race and stopping when there's a whole race to be run for God!
Ultimately, it all comes down to grace and our acceptance of it. We should be so grateful for God's grace that we want to do great things for Him, not take this most precious gift and keep on our mantle.