In Greek culture, it was frowned upon (to put it lightly) for a woman to die during child birth. Are any myths told of a woman dying during child birth? Did the mother dying have any effect on the child's reputation?
If Grimms "Kinder und Hausmärchen" (AKA Grimms Fairy Tales) count, then the obvious tale is "Van den Machandelboom" (AKA "The Juniper Tree"). Mom wished for a child "only a child so red as blood and so white as snow!" Then "she had a child, so white as snow and so red as blood; and when she saw that, so she was so happy, that she died." How long the mother is still alive after the birth is not actually mentioned, but it appears to be right after the birth of the child that she dies.
See also "Sneewittchen" (AKA "Snow White"). After the first edition of the KHM (2nd ed of 1819 and onwards) Snow White's mother dies right after having given birth to her. In the first ed, the mother lives and there is no step-mother character. The beginning is similar to "The Juniper Tree." The mother also says: "if I only had a child so white as snow, so red as blood and so black as this frame."
Well I'm not sure this counts but the story of Semele, where she gets destroyed by Zeus's full glory.
Thyone's mortal name was Semele. She was a Theban princess loved by the god Zeus. When his wife Hera learned of their affair, she tricked the girl into having Zeus swear an oath to appear before her in his full glory. Bound by his pledge the god did so and Semele was consumed by the fire of his lightning-bolts.
(I'm sure if you're on this site, you know about this story well enough.)
The death of his mother did not really affect him as far as I know, he grew up under the influence of two other foster parents without knowledge of his parents, which had other problems, also caused by Hera, and it induced his ability of madness.
Pseudo-Apollodorus, Bibliotheca 3. 29 - 30 :
"Zeus loosened the stitches and gave birth to Dionysos, whom he entrusted to Hermes. Hermes took him to Ino and Athamas, and persuaded them to bring him up as a girl. Incensed, Hera inflicted madness on them. As for Zeus, he escaped Hera's anger by changing Dionysos into a baby goat. Hermes took him to the Nymphai of Asian Nysa, whom Zeus in later times places among the stars and named the Hyades."
Probably not a sufficient answer at all, but whatever
Late to the party, but according to Tv Tropes, this happens three myths; in the Bible, Jacob's wife Rachel dies while giving birth to her son Benjamin and Japanese goddess Izanami dies while giving birth to fire god Kagutsuchi; and the Cyrpian version of Ariadne.
(open the "Religion and Mythology" section.)