The Vatican publishes new teachings all the time. What do Catholics have to believe?
This question addresses two things—teaching and belief—so I want to respond to both. Let's start with belief. Not much has changed in the realm of Christian faith since the time of the apostles, so the Apostles’ Creed is still the best summary of what Roman Catholics and many other Christians declare to be true. In a few lines, it affirms a surprising number of heavyweight doctrines:
—That God is revealed as Trinity
—That Jesus Christ has two natures, human and divine
—The Virgin Birth
—The Paschal Mystery: Jesus suffered, died, and rose again
—The Ascension of Jesus
—Heavenly realities, including final judgment, the communion of saints, and eternal life
—That the church participates in the holiness of God
—The central teaching of the forgiveness of sins
The Nicene Creed, which we profess at Mass, employs the blueprint of the Apostles’ Creed and seeks only to clarify its tenets. It was written at the Council of Nicaea in 325 and revised in 381at the Council of Constantinople. Both "editions" sought to address specific misinterpretations of church doctrine. The most familiar contribution of the Nicene Creed is the four marks of the church: "one, holy, catholic, and apostolic."
At Baptism each new Catholic is asked to affirm the doctrines contained in the Creed (in the case of infants, through their godparents). These are the same beliefs we confirm at every Eucharist.
The elements contained in the Creed are matters of faith. By comparison, the rest of church teaching is a matter of morals. I don't want to suggest that moral teaching is less binding than doctrine. As the Letter of James reminds us, faith and works are intimately woven concerns. What we believe influences the choices we make, and our actions likewise betray our convictions. The ongoing teaching authority of the church (or magisterium) is important because moral discernment is common to every generation and yet constantly evolving in each one. While basic doctrines don't change, their application in new moral situations must continue to be contemplated.
Scripture
John 11:25-27; Hebrews 11:1; James 2:14-18; 1 John 1:1-4
Website
The Theology Library, from the department of theology of Spring Hill College, the Jesuit College of the South: a large collection of documents relating to church, revelation, liturgy, justice, theology, morality, spirituality, evangelization, and religion.
Books
The Church We Believe In: One, Holy, Catholic, and Apostolic by Francis A. Sullivan (Paulist Press, 1988)
Making Disciples: A Handbook of Christian Moral Formation by Timothy O'Connell (Crossroad, 1998)

Alice Camille is a gem among contemporary writers on scripture and Catholic teaching. She has received numerous awards for her books, columns, and exegetical reflections. She received her Master of Divinity degree from the Franciscan School of Theology in Berkeley, where she also served as adjunct faculty in ministry formation, preaching and proclamation. Alice is an author, religious educator, and parish retreat leader. Learn more at www.alicecamille.com.
What does “salvation history” mean?
Why do Catholics believe in the Assumption of Mary?
Why do priests wear vestments?
What is Catholic decision-making?
Catholicism and other religions
Can I come back to the church?
For those who have gone before
Scripture for Mass consumption
Fun for nuns—and priests and brothers, too
Vocation: For all of life, or only "religious life"?
Is my vocation from God or just my imagination?