I'm surprised no one has given you the most simple and direct quote to answer your question. John 3:
3 Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God.
4 Nicodemus saith unto him, How can a man be born when he is old? can he enter the second time into his mother’s womb, and be born?
5 Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God.
No one can be saved outside the kingdom of God. But according to Jesus no one can enter the kingdom of God without being Baptized. Therefore it follows that no one can be saved without being baptized.
Here's another very straightforward scripture. Matthew 28:19 (Again this is Jesus Speaking):
Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
There is simply no way around it. As much as some people would like to believe that you can believe and Christ and then do whatever you want it is simply not the case. God's house is a house of Order and those who will enter into it must obey his laws.