Some Bible verses that back up the Tradition of Infant Baptism:

“Jesus answered, "Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God.”  (John 3:5)

“Peter (said) to them, "Repent and be baptized,  every one of you, in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the holy Spirit. For the promise is made to you  and to your children and to all those far off, whomever the Lord our God will call.”  (Acts 2:38-39)

"One of them, a woman named Lydia, a dealer in purple cloth, from the city of Thyatira, a worshiper of God, listened, and the Lord opened her heart to pay attention to what Paul was saying.  After she and her household had been baptized.... (Act 16:14-15)

"And they said, "Believe in the Lord Jesus and you and your household will be saved." So they spoke the word of the Lord to him and to everyone in his house. He took them in at that hour of the night and bathed their wounds; then he and all his family were baptized at once." (Acts 16:31-33)

Surely infants were baptizes as well.

“He who believes and is baptized will be saved; but he who does not believe will be condemned.”  (Mark 16:16)
                              
“but Jesus said, "Let the children come to me, and do not hinder them; for to such belongs the kingdom of heaven.” (Matt. 19:14)

“Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the holy Spirit”  (Matt 28:19)

“Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? We were buried therefore with him by baptism into death, so that as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life” (Rom. 6:3-4  )

“When Jesus returned to Capernaum ... They came bringing to him a paralytic carried by four men. Unable to get near Jesus because of the crowd, they opened up the roof above him. After they had broken through, they let down the mat on which the paralytic was lying. When Jesus saw their faith, he said to the paralytic, "Child, your sins are forgiven.”  (Mk 2:1-5)

“For as by a man came death, by a man has come also the resurrection of the dead.  For as in Adam all die, so also in Christ shall all be made alive.”  (1 Cor 15:21-22)  "All" would include infants.

"I baptized the household of Stephanas also; beyond that I do not know whether I baptized anyone else." (1Cor 1:16)

“But the free gift is not like the trespass. For if many died through one man's trespass, much more have the grace of God and the free gift in the grace of that one man Jesus Christ abounded for many. And the free gift is not like the effect of that one man's sin. For the judgment following one trespass brought condemnation, but the free gift following many trespasses brings justification.” (Rom 5:15-16  )

“To the woman he said, "I will greatly multiply your pain in childbearing; in pain you shall bring forth children, yet your desire shall be for your husband, and he shall rule over you.”  (Gen 3:16)

"True, I was born guilty, a sinner, even as my mother conceived me."  (Psalms 51:5)

“Before I formed you in the womb I knew you, and before you were born I consecrated you;” (Jeremiah 1:5)  This verse also shows that life begins at conception.

“And you he made alive, when you were dead through the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience. Among these we all once lived in the passions of our flesh, following the desires of body and mind, and so we were by nature children of wrath, like the rest of mankind.  But God, who is rich in mercy, out of the great love with which he loved us, even when we were dead through our trespasses, made us alive together with Christ (by grace you have been saved), and raised us up with him, and made us sit with him in the heavenly places in Christ Jesus,” (Eph 2:1-6)  This passage shows the effect that original sin has on mankind.  Baptism removes this sin which we all inherit from Adam.

Some non-catholic churches believe that full water immersion is the only valid way to baptize.  While full immersion is the fullest expression of baptism it is not the only valid way to baptize.  The Didache, which
is an early church writing, gives an insight to the baptism practices of the early church.  

The Didache:

Chapter 7

7:1 But concerning baptism, thus baptize ye: having first recited all these precepts, baptize in the name of the Father, and of the Son, and of the Holy Spirit, in running water;
7:2 but if thou hast not running water, baptize in some other water, and if thou canst not baptize in cold, in warm water;
7:3 but if thou hast neither, pour water three times on the head, in the name of the Father, and of the Son, and of the Holy Spirit.
7:4 But before the baptism, let him who baptizeth and him who is baptized fast previously, and any others who may be able. And thou shalt command him who is baptized to fast one or two days before.