This condition, Erythroblastosis fetalis, is not the same thing as "blue baby" syndrome¹ (as stated previously in another writeup). It occurs when a mother with Rh- blood type and a Rh+ father have an Rh+ baby. The mother's blood develops antibodies against the Rh+ blood, which attack the fetus' red blood cells. In severe cases, the resulting anemia can cause fetal death.
Otherwise, affected infants will emerge into the world pale and anemic. Other symptoms may include edema (swollen tissues), difficulty in breathing, seizures, and poor reflexes and a general lack of movement.
TheLordScribe is correct regarding the need for immediate transfusion. TheLordScribe is also correct regarding the nature of the phenomenon regarding Rh factors and the second (and subsequent) Rh+ babies. ABO incompatabilities can mitigate or increase the risk, depending on how they interact. Note that Erythroblastosis fetalis can take place even with the mother's first Rh+ baby if the mother was previously exposed to Rh+ blood through transfusion.
The risk can be successfully mitigated by anti-Rh gamma globulin treatments during the 28th week of pregnancy, or by injection of human immune globulin within 72 hours after delivery of the first baby.
Sources: Extensive research after discovering my girlfriend is Rh- ... I'm Rh+ ... Who cares what her blood type is? I do.
1. Methemoglobinemia, or "blue baby" syndrome, results from exposure to nitrate, usually in drinking water. The high pH levels in a baby's digestive system converts the nitrate to nitrite, which inhibit's the red blood cells' ability to carry oxygen. This results in cyanosis and the characteristic blue coloration.