Water Baptism Is a Sign
Mark 16:16 "He that believeth and is baptized shall be saved; but he that believeth not shall be damned."
Water baptism is a command of Jesus and is the initial action taken upon believing. Mark's statement could be rendered, "He who believes with saving faith (i.e. faith that produces actions) will be saved." In this sense, water baptism is very important. It is an opportunity to act on your new profession of faith. Anyone who refuses to follow Jesus' command to receive water baptism, may be suspected of not really believing.
However, there are scriptural examples of people being born again before they were baptized in water. Cornelius and his friends were filled with the Holy Ghost and spoke in tongues before they were baptized in water (Acts 10:44-48). John 14:17 records Jesus saying that an unbeliever cannot receive the Holy Ghost, so Cornelius and his friends must have been born again before their water baptism.
Water baptism is the sign of the new covenant in the same way that circumcision was the sign of the old covenant. The apostle Paul made it clear in Romans 4, that although Abraham was circumcised, his circumcision was only a sign. Abraham was justified in the sight of God before his circumcision. Paul goes on to state in Galatians 5:1-6, that anyone who trusts in circumcision has fallen from grace; Christ will profit him nothing.
It is faith in the redemptive work of Christ that produces salvation - not our actions. However, James writes that faith without works is dead (Jas. 2:20).
Faith alone saves, but saving faith is never alone; it must be acted upon.
This is what Mark is referring to when he speaks of baptism.