There’s two ways to view baptism: sacramental or non-sacramental. Those who view baptism as a sacrament understand it to be a means of grace, i.e., a vehicle through which God confers his grace on the believer. Those who view baptism as a non-sacrament understand it to be an ordinance, i.e., a command given by Jesus that should be obeyed by believers.
One’s view of baptism will determine how they answer the question “Does baptism save?” Those who view it sacramentally will say, “Of course!” Those who view it non-sacramentally will say, “Of course not!” The sacramental view understands the sacraments as something God does that believers get to participate in. The non-sacramental view understands the ordinance as something believers do because God commanded it.
This is why you’ll often find people arguing about “works salvation” when the issue of baptism’s salvific significance comes up. The non-sacramentalists understand baptism as something we do, so it’s a work, and a work can’t save lest it give us reason to boast. The sacramentalist, on the other hand, sees it as something God has done in order that we may be saved, so there’s no reason to boast since the work is Christ’s and we’re simply allowed union with it.
And this, of course, determines how we read passages like 1 Peter 3:21; John 3:5; Acts 2:38; and Mark 16:16, among others. The sacramentalists take these verses at face value. Baptism saves. Baptism is necessary for the forgiveness of sins. Non-sacramentalists have ready objections: the passage in Mark may not be original, but even if it is, it doesn’t say that one who doesn’t believe and is not baptized will condemned; 1 Peter is speaking symbolically; Jesus spoke of natural birth with his reference to being born of water; etc.
Where do you stand on the question? Does baptism save, and if so, in what way?