I was at my BFF's, poking around my family tree (she's a family history fiend) and we were merging a record-- or something; she was showing me how, and I was doing what she said to, but not necessarily following everything. Anyway, we found a census record showing a Maude Greenhaw in this family, aged five, in 1900. The family record only showed her as having been born, then died only a few days later, in 1903.
Now, I know enough to be aware that sometimes families would name a child after an earlier one who had died; but this seemed... odd. So we looked at her death record, which was a death certificate uploaded to find-a-grave. Lo and behold, she died and was buried a few days apart in 1903; but her age at the time of death was eight years and twenty-four days!
So I corrected the record in FamilySearch, and I put in notes about why it had been one way and why I was pretty sure it should be the other way; and, through the magic of computers and the internet, I reserved the privilege of being baptized for and in behalf of my great-great-aunt (if I counted that right).
As a Mormon, my belief is that children who die before the age of eight go straight back to their Heavenly Father, no questions asked; they aren't old enough to make their own meaningful choices, and the Atonement of Christ automatically covers them. At eight years and twenty-four days, however, Maude was old enough to have understood and accepted the covenant of baptism-- a choice she would need to make in order to be accepted into the Kingdom of God, as Jesus explained to Nicodemus. By being baptized for an in behalf of her, I didn't force her to accept that baptism; I just gave her the opportunity to accept it. This is very similar to how the Atonement of Jesus Christ gives us the option to repent, but does not force us to.