Yes, Catholics are Christian, as are Protestants and Eastern Orthodox Christians. A Christian is someone who professes the belief that Jesus Christ is the Son of God and that He is Lord and Savior of mankind.
Christians believe in the divinity of Christ and in His humanity (that Jesus is God and Man). They also believe in the doctrine of the Holy Trinity, that there is only One God, yet that one God is also three Persons (Father, Son, and Holy Spirit). Catholics also believe, as do all Christians, that the Bible (sacred scripture) is the inspired, inerrant written Word of God.
Some non-Catholic Christians accuse Catholics of not being Christian because they misinterpret some Catholic teaching or practice and judge it to be contradictory to Christian belief. For example, Catholics do not worship Mary, but are accused of it often.
Catholicism does not see itself as another variety of Christianity as many Protestant denominations see themselves. Catholics are not better, smarter, holier, or more fun than Protestants, Orthodox, Jews, or Muslims. Catholicism as a religion does see herself as having and providing more for her members, and the Church believes she can give all that her members need for their spiritual life.