Alright! A bit of [historically] Catholic dialectic:
Original sin is that whereby the human race lost the original justification possessed by Adam and Eve. Human nature now exists in a fallen state. AMR and the calvinists err in appealing to original sin to justify the torment of infants, since original sin merely indicates a general fallen state of humanity. It's not personal sin.
Personal sin, on the other hand, is that whereby each individual commits a moral wrong and separates himself from God. Personal sin carries both personal guilt and the need to be punished for it. Personal sin, strictly speaking, is that which is punished in Hell.
Babies, whereas they are born into original sin, are not born with any personal sin. Therefore, if they die unbaptised, they can't be punished for anything. That would be unjust. I believe that St. Augustine says that unbaptised babies go to Hell, but I also believe that he qualifies this by saying that their condition is so mild that it's not particularly unpleasant.
This isn't necessarily an unreasonable position, if we remember that Hell is ultimately separation from God. Through Adam, all men have been separated from God. Therefore, one might indeed reason, all men deserve Hell. It must be pointed out, however, that this must be qualified: "but the punishments must still be according to your deeds." Babies aren't personally evil; therefore, even if they go to Hell, they cannot be punished.
That said, it's still an unpalatable position.
For this reason, in the middle ages, a middle state called "limbo" came to be postulated. Suppose it's unfair for babies to go to Hell. They still don't deserve to go to Heaven. Nobody deserves Heaven. Heaven is a supernatural gift of grace; it's something that exceeds what properly belongs to human nature. Well, there's just gotta be something in the middle, right?
Babies don't deserve Hell. Hell is the degradation of human nature, and babies have done nothing to degrade themselves. Babies also don't deserve Heaven. Heaven is a supernatural gift of grace over and beyond human nature. We shouldn't necessarily conclude that all babies receive these supernatural gifts of grace; otherwise, there would be no point in baptising babies.
There must, so many of the medievals concluded, be a middle state which properly belongs to human nature as it stands on its own. Some middle state which neither is the degradation of human nature (Hell) or the supernatural gift over and beyond it (Heaven), but rather a state where babies are made as happy as human nature in its "natural" state permits. This is called "limbo."
As a Platonist, I've come to see certain problems with this doctrine (it's clearly an Aristotelian advance), but I don't think that it can be ruled out altogether.
If nothing else, it helps to put things into perspective, namely, exactly what issues are at stake.