Blessed John Paul II admonished Christian parents in 1980 that they should not delay baptizing their newborn infants. The Holy Father said that infants should be baptized immediately if the child appears in danger of death. Otherwise, the infant should be baptized "within the first weeks after birth." Here's the full quote:
Accordingly, if the child is in danger of death, it is to be baptized without delay. Otherwise, as a rule an infant should be baptized within the first weeks after birth (Blessed John Paul II, Instruction on Holy Baptism, October 20, 1980).
Moreover, the current "Order for Baptizing Infants," states that the baptism of infants should occur within the "first few weeks" after birth (Praenotanda, no. 8, par. 1, p. 17).
It's worth noting that our current Pontiff, His Holiness Pope Benedict XVI, was baptized on the very same day as his birth! No delay whatsoever.
Pope Eugene IV (reigned 1431-1447) taught that infants should be baptized within the first "forty days" after birth.
The urgency of infant baptism is reemphasized by the Catechism of the Council of Trent which teaches the same:
The faithful are earnestly to be exhorted to take care that their children be brought to the church, as soon as it can be done with safety, to receive solemn Baptism. Since infant children have no other means of salvation except Baptism, we may easily understand how grievously those persons sin who permit them to remain without the grace of the Sacrament longer than necessity may require, particularly at an age so tender as to be exposed to numberless dangers of death.Here's a YouTube video of the baptism of my new baby Blaise Christopher born on May 12, 2011 and baptized on May 14. He was baptized about 56 hours after birth in the old 1962 Latin rite - Deo gratias!. The video also features the "Churching of Women" for my wife in which she is blessed and consecrated to Jesus and Mary. The video has notes and explanations along the way in case you've never seen the old pre-Vatican II baptism:
Also, here is a great recorded mp3 homily on baptism and the need to baptize babies sooner rather than later: "The Importance and Urgency of Holy Baptism."
While you're at it, check out this excellent sermon on the need for the sacrament of Confirmation: On Confirmation. It explains how Saint Vincent Ferrer prophesied that during the reign of the Antichrist, those without the sacrament of Confirmation will lose their faith and apostatize.