Is baptism necessary for salvation?

No. Faith in Jesus is sufficient for salvation. You don't have to do anything. Christ has done it all. However, baptism is very important and all believers should be baptized. If you refuse baptism after salvation, I would doubt your conversion.
There are denominations that believe baptism is necessary for salvation. The arguments used, on the surface, seem to be powerful. However, upon examination, baptism is found to occur after conversion, and is not in any way a cause or part of it. Take, for example, Acts 10:44-47. While Peter was witnessing, the Holy Spirit fell upon all those who were listening to the message...and they were hearing them speaking in tongues and exalting God. Then Peter answered, "Surely no one can refuse the water for these to be baptized who have received the Holy Spirit just as we did, can he?"
This passage shows that baptism happens after salvation. How do we know they were saved? They were speaking in tongues -- which is a gift from God to believers (1 Cor. 14)and they were exalting God. Non-believers do not exalt God. Also, Peter said they had received the Holy Spirit. That is only for Christians, and it happened before baptism. (Note: speaking in tongues is simply a sign of salvation. It is not necessary that a Christian speak in tongues as a proof of salvation. Not all speak in tongues (1 Cor. 12:30).
Another set of verses applicable to this issue is 1 Cor. 1:17. Paul says, "For Christ did not send me to baptize, but to preach the gospel..." The gospel is what saves, and it is explained in 1 Cor. 15:1-4. Baptism is not part of the gospel; it is something that the believer does after salvation.
Baptism is only a symbol of that which saves, and symbols don't save.
There are no verses that say that baptism is necessary for salvation or say that if you do not get baptized you are condemned. But there are verses that say if you don't believe you are condemned. So, baptism is important, but it is not necessary to be saved.
If baptism is necessary for salvation then babies who die in the womb, during birth, or right after birth could not be saved. It would also mean that anyone who receives Christ on his deathbed and dies before getting baptized would go to hell. It would mean that faith is not what saves you.