Quaeritur: I have entered into a (friendly) debate on abortion and someone asked me what the Catholic Church teaches about the eternal destiny of the souls of aborted babies. I'm a recent convert, so I wanted some help before I reply. Grazie!
Respondeo: Most Catholics today sadly just canonize the souls of aborted babies, assuming that since they never sinned, they automatically go to Heaven. But they either forget original sin and the necessity of Baptism, or gloss over these problems by citing God's mercy as the demonstrative proof that they are in fact in Heaven, regardless of what God may have revealed on the matter. But in fact, there is a sharp discrepancy between these new theological tendencies (promoted by the nouvelle theologie) and what the sources of Revelation have to say on the matter.
The sources of Revelation all point to the concept of the 'Limbo of Children' (limbus puerorum)---to be distinguished from the 'Limbo of the Fathers' (limbus patrum), which is where Christ descended after his death. Limbo itself is not a dogma (i.e., not de fide, but only sententia certa or even a doctrina catholica); but it it is derived from other revealed doctrines that are de fide definita, such as the impossibility of salvation for those who die in original sin.
First of all, it is a defined dogma that souls of those who die in the state of original sin but without having committed actual sins (this includes generally those who die without Baptism and before the age of reason) cannot enter Heaven. However, they do not suffer the bodily pains of hell either.
Pope Gregory X, in the 2nd Council of Lyons, declared:
“Now, the souls of those who depart in mortal sin, or only with original sin, immediately descend into hell, but to be punished differently” (Denzinger 464 [858]).
This doctrine was infallibly defined and ratified by Eugenius IV, in the Concil of Florence (cf. Denzinger 693 [1306].) This dogma, that souls with original sin only are punished differently from those which die in mortal sin, is the basis for the constant teaching of the theologians on Limbo. You can read a pretty thorough theological defense of Limbo that cites the authority of the theological sources, including the Magisterium and the consensus of approved theologians throughout the centuries, here.
Now, this is not to say that Limbo is a third eternal destiny, in addition to Heaven and Hell, as is often erroneously supposed. This hypothesis, that Limbo is a distinct state besides Heaven and Hell, was actually condemned: at the end of time, only two states will remain: Heaven and Hell. (Oddly, I've heard and read fallacious arguments that try to refute the existence of Limbo by citing the condemnation, thinking that what is condemned is Limbo itself. But in reality what is condemned is the claim that Limbo is a third state distinct from Heaven and Hell; see Pius VI, Auctorem Fidei; Denzinger 1526 [2626].). No, Limbo is in fact part of Hell. It involves the eternal loss of the Beatific Vision, which is the essence of Hell, even if it does not involve the horrible physical sufferings that we usually associate with Hell and which are only an accidental aspect of the latter.
St Thomas Aquinas specifically distinguishes in hell the punishment or 'pain' of sense (poena sensus) from the punishment of separation or loss (poena damni), which is not really 'pain' at all: souls with actual mortal sins suffer both, but souls with original sin only, are only subject to the latter: they do not see God face-to-face, but they do enjoy a natural sort of happiness where their natural powers (intellect, will, etc.) and body are fulfilled to their natural capacities. And this is known to the faithful by the term 'Limbo' (from the Latin, limbus, border), and was popularized in Catholic imagination by Dante, who wonderfully describes Limbo as the 'first circle' of hell. (See Summa theologiae Ia-IIae, q. 87, a. 4; IIIae Supp., q. 97, a. 5.)
That's the traditional teaching, but as you can see, it is considered to be a bit harsh for modern sensitivities and so there has been a push within contemporary theology, especially within the nouvelle theologie to replace it with a more 'merciful' view (sound familiar?). Some contemporary theologians theorize that just as there can be a 'baptism of desire' on the part of adult catechumens who die without Baptism, and we thus hope for their salvation, so there could be a sort of 'vicarious' baptism of desire for those babies who die without Baptism but whom the Church desires to baptize.
The Catechism of the Catholic Church, which is steeped in the nouvelle theologie, somewhat dodges the issue (and fails to teach the traditional doctrine of Limbo) in paragraph 1261. In the immediately preceding paragraphs it is noticeably 'soft' on the necessity of Baptism for salvation (as compared to the Catechisms, encyclicals, doctors, theologians, etc. of the previous millenia). And in this context it goes on to state that the Church entrusts the souls of those who die in original sin only to the mercy of God:
These hypotheses are problematic. At heart they seem motivated by a characteristically modern (and partly erroneous) idea of divine justice and of the gratuitousness of salvation; and in the case of some theologians, even perhaps an implicit denial of the reality of original sin. Modern minds find it inconceivable that God would deprive an 'innocent' baby of Heaven. After all--they claim--these babies have done nothing wrong, so why would God deprive them of what they were made for? Wouldn't it be unfair for God to damn them in Hell? 1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: "Let the children come to me, do not hinder them" (Mk 10 14; cf. 1 Tim 2:4), allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism.
But, you see, lurking behind the scenes here are two very erroneous assumptions: (a) original sin doesn't really take away these souls' innocence; and (b) God owes it to them to save them, because presumably salvation is what a soul deserves by nature, by default, so long as it does not lose this right by sinning. But of course, these presuppositions are false and heretical. (Most theologians would not dare to state them explicitly; but naïvely the general population does buy into them.) Despite our sensibilities to the contrary, Catholic dogma tells us that these souls are not innocent, but bear the stain of sin and are thus unworthy of the glory of Heaven. Morevoer, God does not owe Heaven to anyone anyway; salvation is a free gift and no one really deserves it (or merit it de condigno). And, what's more, rather than there being some sort of 'unfairness' by assigning to them this eternal lot, God is in fact being merciful towards these souls. God is not punishing them for something they didn't do, but is mercifully granting them an eternal and superabundant natural happiness that they do not deserve. Divine justice, original sin, the gratuity of salvation: we may not like these doctrines, but it's what God revealed. If we really believed in them, we would not find shocking the doctrine of limbo that is widely taught to us by the Catholic tradition throughout the ages, and we wouldn't need to replace it with some vain 'hope' devised to fit our un-Catholic sensibilities.