According to this article from The Times (that's THE Times), a commission that the Pope commissioned to come up with a “more coherent and illuminating” doctrine than limbo will recommand that Limbo be replaced by the more “compassionate” doctrine that all children who die do so “in the hope of eternal salvation”.
I think there is a lot of confusion about limbo that deserves to be addressed. First of all, it was never a "fourth state" besides heaven, hell, and purgatory. Limbo is and always has been a part of hell. A comparatively pleasant part of hell (so they speculated), mind you, but a part of hell, nonetheless.
It comes from the question of, if all men are fallen, and in need of salvation (which normatively speaking begins with baptism), what happens with babies who have no actual sin (i.e. sins committed by an act, as opposed to original sin), but die without baptism in the state of original sin (that is, separated from God)?
I think the situation of babies who would have been baptized but died before their parents had the chance to is fairly clear — what we have here is baptism by desire, same as if a catechumen dies.
Murkier is the situation where a child, say born into a non-religious family, dies before the age of reason. At one point, the general consensus was that such a child dies in the state of original sin, and if you die in the state of original sin, it's an article of faith that you go straight to Hell.
The church is now being more nuanced about it, saying that we merely "commend them to the mercy of God." Certainly, it is possible for God to work outside the confines of the sacraments. Having a well-founded hope that he does as a general case is another issue. There is nothing wrong with commending such children to the mercy of God, as it goes, and we ought to do so. But let's not forget that such mercy would be extraordinary, and not assume it's a given.
By the way, some fundamentalists and Evangelicals, surprisingly enough, do not believe in Original Sin in this sense that all men are implicated in the guilt of Adam. They believe that men are fallen, yes, in the sense that they cannot not sin, but they do not believe that children under the age of reason are in need of salvation. For them, having committed no sin means they do not need salvation. Hence for them, every child that dies under the age of reason goes to heaven automatically.