Today's first reading at Mass is from St Paul's letter to the Ephesian Christians. He tells them that they are not saved "by good works". Catholic theology has no disagreement with that. Protestants, however, say otherwise (I guess they know more about what we believe than we do!). According to most protestants, Catholic theology says that we are each saved by our own works, and some even go so far as to say that do not believe we need Jesus' salvation!
Interestingly, protestant explanations of this passage of Scripture go beyond the text. Just a few verses after saying we are not saved "by good works", St Paul tells us that we are saved "for good works". Quite an interesting twist. We do good works; they do not save us, but they are still a part of our salvation. The distinction is important. We are not supposed to be living our lives apart from good works (like many protestants claim), but we also do not rely on the works themselves to save us. Only Jesus saves us, but He does so in order for us to be able to do good works.
In fact, we can go one step further. The text even says that God "prepared the good works beforehand" for us to do! That is pretty amazing when you think about it. That means that if He prepares something, and we fail to do it, then we are working against Him. He has set up the circumstances in our lives so that we can do "this good work over here" and "that good work over there". He wants us to be living faithfully; not to earn our right standing with Him, but so that we can spread His Kingdom throughout the world.
Therefore, do good works. Do them for the right reason. And, do not let anyone tell you otherwise.