Children, whether born or unborn, who die without baptism of water. The difficult question of whether they can attain the beatific vision in heaven has been discussed for centuries and has become especially grave since abortion is now legalized in so many countries. There is no unqualified answer to this question from the Church's magisterium. But there are two principles of Catholic doctrine that must be reconciled.
On the one hand, the Church teaches that even those who die with only original sin on their souls cannot reach the beatific vision. The Second Council of Lyons (1274) and the Council of Florence (1438-45) explicitly define that those who die with "only original sin" (Peccato vel solo originali) do not reach heaven. There is also the Church's condemnation of the Jansenists, who claimed that it is a myth to hold there is a place "which the faithful generally designate by the name of the limbo of children," for the souls of those who depart this life with only the guilt of original sin (Pius VI, Errors of the Synod of Pistoia, Proposition 26, August 28, 1794).
On the other hand, we also know that, according to God's universal salvific will, somehow he gives all persons the opportunity of reaching heaven. This is authoritatively expressed by the Second Vatican Council in its Dogmatic Constitution on the Church: "Those who, through no fault of their own, do not know the Gospel of Christ or His Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do His will as they know it through the dictates of their conscience--those too can achieve eternal salvation" (Lumen Gentium, 16). By implication, their children who die before the age of reason can also be saved.
Saying all of this, one shouls emphasize how deeply the Church is concerned that children be baptized as soon after birth as possible. "As for the time of Baptism," the Roman ritual states, "the first consideration is the welfare of the child, that it may not be deprived of the benefit of the sacrament." Therefore, "if the child is in danger of death, it is to be baptized without delay."