No more than swimming saves you.
Baptism is never presented in the Scriptures as saving anyone. When baptism is mentioned in the context of salvation, you will always find it paired with something else that would demonstrate belief. But don’t stop here. The rest may be of great importance to your position.
In Mark 16:15-16, Jesus said that those who believe and are baptized would be saved.
There is much controversy (unnecessarily, I believe) over the question of baptism’s place in salvation. I believe that my next comments may disagree with Todd’s beliefs, but they are presented with all respect to his understanding and love for him and his work. I find that I must teach what I understand to be the truth.
In addition to the reference in Mark, and the numerous instances of baptism with respect to salvation in the New Testament (1 Peter 3:21, etc.), I look back to the Old Testament, 2 Kings chapter 5.
In this instance, we find Namaan. He has leprosy. He is informed about a prophet in Israel who can help. After a roundabout route, including a visit to the king, he winds up at the house of Elisha, a prophet of God. Without coming out of the house, Elisha sends a messenger to instruct Namaan to wash himself in the Jordan River seven times and he would be clean. Namaan was furious and refused, citing rivers in the North that were better. His escorts asked him, “If the Prophet asked you to do something hard, would you do it? Why then do you refuse when he says wash and be clean?” Namaan gives in, washes seven times and is clean.
My reasoning is this: What if he had not washed? Would Namaan have been cleansed? The obvious answer is no, he would have died a leper.
Jesus himself said that those who believe and are baptized would be saved. A further New Testament study reveals what He means by this. Evidence of our belief is in our actions, not our words. This action results in the bearing of fruit as we are led by the Holy Spirit to act–not doing works to be saved, but because we are saved (see James). There are no works that can save us.
Thus a dilemma: Is baptism a work? I vote no. Using reasoning that baptism is a work could just as easily reason that faith or belief in Jesus is a work. You have to do it or there is no salvation. Baptism is a faithful response to an offer of eternal salvation and a declaration of that faith, just like Namaan. Was it the washing that cleansed him? No, it was his faithful response to an offer of cleansing.
Regardless of your belief in the role of baptism in salvation, Jesus himself commanded it. The apostles many times reiterated this command and practiced it. We can do no less. But do not view baptism as saving you. Only Jesus can do that and even so, only through our faith. I say respond.