Baptism and regeneration
'Born of water and the Spirit' with 'repent and be baptized' (Acts 2:38), the washing of rebirth (Titus 3:5) and the saving of 1 Peter 3:21 — regeneration in baptism or a sign received by faith.
John 3:1-8
1Now there was a man of the Pharisees named Nicodemus, a ruler of the Jews.
2The same came to him 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.”
3Jesus answered him, “Most certainly, I tell you, unless one is born anew, he can’t see God’s Kingdom.”
4Nicodemus 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?”
5Jesus answered, “Most certainly I tell you, unless one is born of water and spirit, he can’t enter into God’s Kingdom.
6That which is born of the flesh is flesh. That which is born of the Spirit is spirit.
7Don’t marvel that I said to you, ‘You must be born anew.’
8The wind blows where it wants to, and you hear its sound, but don’t know where it comes from and where it is going. So is everyone who is born of the Spirit.”
What each tradition says
Rabbinic / Midrashic
R. Akiba, in the second century, applied Ezekiel 36:25 to Israel’s cleansing, asking before whom Israel cleanses itself and who cleanses it. His answer is Israel’s Father in heaven, so he calls Israel blessed.
Kaufmann Kohler (1843-1926) and Samuel Krauss (1866-1952), The Jewish Encyclopedia, vol. 2, s.v. 'Baptism' (New York: Funk & Wagnalls, 1901-1906) — article body, on Ezek. xxxvi. 25
Patristic
Cyril of Jerusalem teaches that in going down into the water, do not think of the bare element but look for salvation by the power of the Holy Ghost. Without both, he says, you cannot possibly be made perfect.
Cyril of Jerusalem (c. 313-386), The Catechetical Lectures, Lecture III ('On Baptism'), in Nicene and Post-Nicene Fathers, ser. 2, vol. 7 (trans. Edwin Hamilton Gifford; Oxford: James Parker, 1894) — Lecture III, §4 (before the appeal to John iii. 5)
Catholic
The Council of Trent states that true and natural water is necessary for baptism. It declares anathema on anyone who denies this or turns Christ's words "Unless a man be born again of water and the Holy Ghost" into some sort of metaphor.
The Council of Trent, Session VII (1547), The Canons and Decrees of the Sacred and Oecumenical Council of Trent (trans. J. Waterworth; London: Dolman, 1848) — Session VII, canons on Baptism, canon 2
Orthodox
The Synod of Jerusalem says that without it none is able to be saved. As the Lord says, “Whosoever is not born of water and of the Spirit, shall in no wise enter into the Kingdom of the Heavens.”
The Synod of Jerusalem (1672), under Patriarch Dositheus, The Acts and Decrees of the Synod of Jerusalem, sometimes called the Council of Bethlehem, holden under Dositheus, Patriarch of Jerusalem, in 1672 (trans. J. N. W. B. Robertson; London: Thomas Baker, 1899) — Confession of Dositheus, Decree XVI
Reformed / Protestant
Calvin says we should not press Christ's words to confine salvation to the outward sign. The water is connected with the Spirit, because under that visible symbol he attests and seals the newness of life God alone produces by his Spirit. Neglecting baptism excludes from salvation; still, the hope of salvation is not confined to the sign.
John Calvin (1509-1564), Commentary on the Gospel according to John, vol. 1 (trans. William Pringle; Edinburgh: Calvin Translation Society, 1847) — Commentary on John 3:1-6, comment on verse 5
Evangelical
Albert Barnes identifies the water in John 3:5 as baptism, as also in Ephesians 5:26 and Titus 3:5. He notes baptism was practiced by Jews in receiving a Gentile as a proselyte and by John among the Jews; Jesus says it is an ordinance of his religion and the sign and seal of the renewing influences of his Spirit.