​Is water baptism involved in salvation?

No, there are many clear verses showing otherwise.  Among the most clarifying is this passage, which shows a procedure starting with baptism of the Holy Ghost (which happens when someone is saved) followed by baptism in water:
  • ¶ While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God. Then answered Peter, Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days. (Acts 10:44-48)
We see this same procedure a couple of chapters earlier in Acts:
  • And as they went on [their] way, they came unto a certain water: and the eunuch said, See, [here is] water; what doth hinder me to be baptized? And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God. And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him. (Acts 8:36-38)
(Sidenote: As most modern Bible versions are based on the Alexandrian line of manuscripts which are more supportive of Catholic doctrine, verse 37 (showing belief comes before water baptism) is missing from many or most of these newer Bibles.  Just another reason to go with the good old KJV.)

To bring in another Apostle, what was Paul's mission from Jesus?
  • ¶ For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect. (1 Corinthians 1:17)
If water baptism were so important to be saved, why wasn't that included in Paul's mission directive?

Proponents of baptismal regeneration also promote John 3:5 to strengthen their case:
  • 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. (John 3:5)
However, we can gather necessary context by simply examining the verse before and after it:
  • 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? (John 3:4)
  • That which is born of the flesh is flesh; and that which is born of the Spirit is spirit. Marvel not that I said unto thee, Ye must be born again. (John 3:6-7)
Surely it's possible to see that being born of water can mean being born from a mother (of the flesh, from the watery Amniotic sac), and that the context strongly supports that interpretation.

​And these two baptisms (of water and of the Spirit) are shown to be different and independent elsewhere:
  • And preached, saying, There cometh one mightier than I after me, the latchet of whose shoes I am not worthy to stoop down and unloose. I indeed have baptized you with water: but he shall baptize you with the Holy Ghost. (Mark 1:7-8) 
  • For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence. (Acts 1:5) 
  • Who shall tell thee words, whereby thou and all thy house shall be saved. And as I began to speak, the Holy Ghost fell on them, as on us at the beginning. Then remembered I the word of the Lord, how that he said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost. Forasmuch then as God gave them the like gift as [he did] unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God? (Acts 11:14-17) 
As you can see in Acts 11:17, the gift is the baptism of the Holy Ghost, and it's given to those who believed on the Lord Jesus Christ.  As those who believe on the Lord Jesus Christ are saved, then you can again see in Acts 10:45 in the first section above that they were saved before they were baptized in water.

Some people will also bring up verses like Acts 2:38, saying that water baptism is required for the remission of sins because the word "for" makes that necessary:
  • Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost. (Acts 2:38)
But that's assuming "for" means something like "in order to receieve," but "for" can also mean something like "because of."  Here are two examples of that:
  • ¶ And it came to pass, when he was in a certain city, behold a man full of leprosy: who seeing Jesus fell on [his] face, and besought him, saying, Lord, if thou wilt, thou canst make me clean. And he put forth [his] hand, and touched him, saying, I will: be thou clean. And immediately the leprosy departed from him. And he charged him to tell no man: but go, and shew thyself to the priest, and offer for thy cleansing, according as Moses commanded, for a testimony unto them. (Luke 5:12-14) 
  • ¶ And there came a leper to him, beseeching him, and kneeling down to him, and saying unto him, If thou wilt, thou canst make me clean. And Jesus, moved with compassion, put forth [his] hand, and touched him, and saith unto him, I will; be thou clean. And as soon as he had spoken, immediately the leprosy departed from him, and he was cleansed. And he straitly charged him, and forthwith sent him away; And saith unto him, See thou say nothing to any man: but go thy way, shew thyself to the priest, and offer for thy cleansing those things which Moses commanded, for a testimony unto them. (Mark 1:40-44) 
The leper didn't need to receive cleansing from the priest, he was already clean.  But he could have offered the things which Moses commanded to the priest because of his cleansing.  So in Acts 2:38, the meaning could be more along the lines of: everyone there should have been baptized in water because of the remission of their sins.  The remission of sins would have happened when they repented, or changed their mind to believing the gospel, at which time they would have been baptized by the Holy Ghost.

We find another verse that's used to teach baptismal regeneration in Mark 16:16:
  • He that believeth and is baptized shall be saved; but he that believeth not shall be damned. (Mark 16:16) 
Take notice of what's required to be damned.  To not believe.  One can believe and join a church and be saved, or they can believe and feed the poor and be saved.  The condition for salvation is nonetheless belief.  I think it's also possible that this could be the baptism of the Holy Ghost that's spoken about, but I'm not sure, and it need not be to reject salvation by water baptism.

Yet another verse used by the baptismal regeneration camp is the one where Paul says there's one baptism.  I think this is, from the context, talking about what unites Christians:
  • ¶ With all lowliness and meekness, with longsuffering, forbearing one another in love; Endeavouring to keep the unity of the Spirit in the bond of peace. [There is] one body, and one Spirit, even as ye are called in one hope of your calling; One Lord, one faith, one baptism, One God and Father of all, who [is] above all, and through all, and in you all. (Ephesians 4:2-6)
And if there's only one baptism, and we're baptized by the Holy Spirit when we're saved (whether we feel anything or not), then that would be the one baptism that all Christians share.
  • For by one Spirit are we all baptized into one body, whether [we be] Jews or Gentiles, whether [we be] bond or free; and have been all made to drink into one Spirit. (1 Corinthians 12:13)

Lastly, there's a verse comparison that disproves baptismal regeneration.
See how Jesus suggests that water baptism is a work of righteousness:
  • ¶ Then cometh Jesus from Galilee to Jordan unto John, to be baptized of him. But John forbad him, saying, I have need to be baptized of thee, and comest thou to me? And Jesus answering said unto him, Suffer [it to be so] now: for thus it becometh us to fulfil all righteousness. Then he suffered him. (Matthew 3:13-15) 
And compare that to what we can do to be saved:
  • Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost; (Titus 3:5) 

So, to summarize and repeat a bit, when you believe the gospel your sins are forgiven and you're baptized by the Holy Ghost.  Then you have the option of being baptized in water.

I'm not saying water baptism isn't important and something I think God wants us to do, but that it is separate from and should only come after salvation.  It seems to be a symbol of how we have died as Christ died on the cross (when we go into the water), were buried as Christ was (are in the water), and will rise again as Christ did (come out of the water).  And the person baptising the believer represents Christ.  It lets others know about what's happened to us.  And that's good to do, as one of the best things we can do in this world is to reach out to others for God and to get them saved, too.
  • Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, [even] unto the end of the world. Amen. (Matthew 28:19-20)