If we take the verse (John 3:5) in context, we can see that being "born of water" has nothing to do with baptism. The water birth is referring to the "water" that breaks as a part of the natural birth process when a woman gives birth to a child. People who hold to an over-emphasised doctrine on water baptism may have a hard time reading the proper context but give it a try:
John 3:1-6 Now there was a man of the Pharisees named Nicodemus, a ruler of the Jews. (2) This man came to Jesus by night and said to him, "Rabbi, we know that you are a teacher come from God, for no one can do these signs that you do unless God is with him." (3) Jesus answered him, "Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God." (4) Nicodemus said to him, "How can a man be born when he is old? Can he enter a second time into his mother's womb and be born?" (5) Jesus answered, "Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. (6) That which is born of the flesh is flesh, and that which is born of the Spirit is spirit.
We are all born of the flesh, which corresponds to the natural birth, or being born of water. Only those who are saved by God are born again via the spirit.
If we take the water birth to be the Christian baptism here, then we must also take the spirit birth to be baptism of the spirit. That gives us two baptisms that we must undergo to enter the kingdom, yet if this is true we have a contradiction in scripture because there is "...one Lord, one faith, one baptism..." Ephesians 4:5
I freely admit that I was thoroughly confused over the conflict between these two verses for many years. When I first read this I feared that I wasn't saved because I hadn't been baptised, but at the same time I knew that salvation was a spiritual work of God. It wasn't until I spent some time meditating on John chapter 3 that it finally clicked. Boy did I praise God for the understanding that he had granted me, after being frustrated for so long!
I hope this helps others also!