Westminster Larger Catechism

Question 165: WHAT is Baptism?

Answer 165: Baptism is a sacrament of the New Testament, wherein Christ hath ordained the washing with water in the name of the Father, and of the Son, and of the Holy Ghost, to be a sign and seal . . .
  of ingrafting into himself,
  of remission of sins by his blood,
  and regeneration by his Spirit;
  of adoption, and resurrection unto everlasting life;
and whereby the parties baptized are solemnly admitted into the visible church, and enter into an open and professed engagement to be wholly and only the Lord's.

Question 166: Unto WHOM is Baptism to be administered?

Answer 166: Baptism is not to be administered to any that are out of the visible church, and so strangers from the covenant of promise, till they profess their faith in Christ, and obedience to him, but infants descending from parents, either both, or but one of them, professing faith in Christ, and obedience to him, are in that respect within the covenant, and to be baptized.

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Westminster Confession of Faith

Chapter XXVIII - OF BAPTISM

I. Baptism is a sacrament of the New Testament, ordained by Jesus Christ, not only for the solemn admission of the party baptized into the visible Church; but also, to be unto him:
  a sign and seal of the covenant of grace,
  of his ingrafting into Christ,
  of regeneration,
  of remission of sins,
and of his giving up unto God through Jesus Christ, to walk in the newness of life. Which sacrament is, by Christ's own appointment, to be continued in His Church until the end of the world.

IV. Not only those that do actually profess faith in and obedience unto Christ, but also the infants of one or both believing parents, are to be baptized.

VII. The sacrament of Baptism is but once to be administered unto any person.

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Charles Spurgeon made the following comments about "infant baptism" —

The addition of "infant baptism" to the Word of God — for it certainly is not there — is fraught with mischief!

Without faith or even consciousness, as in the case of babes — how can spiritual benefits be connected with the sprinkling of water?

'Baptismal regeneration' rides in upon the shoulders of infant baptism!

We find a class of people who are the children of former converts, and who have been baptized as infants, and are therefore called Christians. But they are not one whit better than the heathen around them! They seem to think that they are Christians because of their infant baptism; and at the same time, being thought Christians by the heathen--their evil lives are perpetual scandal and a dreadful stumbling-block!

May God give us that vital, essential faith, without which there is no salvation.

Baptized, re-baptized, circumcised, confirmed, fed upon sacraments, and buried in consecrated ground — you shall all perish except you believe in Him!