How much of an education one is obligated to provide for his children: Kiddushin 30a
Whether the obligation to educate a child extends to the child's grandfather: Kiddushin 30a
HaShem puts a person who doesn't raise his children to learn Torah in Ex-Communication: Pesachim 113b
Teaching one's children merits The "World to Come": Pesachim 113a
One should teach [his child] out of a well-edited book, because once an error is learned, it is hard to correct it: Pesachim 112a
Requirement of teaching one's son: Berachot 13b
Whether one's personal obligation to learn has priority over the obligation of having his child taught, or not: Kiddushin 29b
Whether the requirement of teaching one's son is upon both parents, or only the father: Kiddushin 29a, 29b Reward for teaching one's child is in this world and in The "World to Come": Shabbat 127a
Considering teaching one's son Torah, to be like teaching it to all future generations: Kiddushin 30a
Equating the teaching of Torah to one's grandchild, to receiving the Torah at Sinai: Berachot 21b; Kiddushin 30a
Male children require more watching than female children do, when they are supposed to be studying: Nedarim 37b
Disciplining one's children, for purposes other than to coax them into learning: Makkot 8a, 8b [2x]
General Issues
A specific age of Education: R. Berachot 15b "Bameh Devarim"
Teaching a child a path which he will use his entire life: Kiddushin 30a
Mitzvah of Education applies for any Mitzvah where an adult would have a Biblical Requirement to keep that Mitzvah: Chagigah 6a
Education of a Minor for a Mitzvah in which he is ineligible for a reason besides Age, but for which he may be eligible in the future: Chagigah 6a
Not striking an adult child, because it could lead him to sin in striking back: Moed Katan 17a Accidental murder of a child while disciplining him: Makkot 8a
Specific Cases
Giving children bread after making the Blessing for them, to teach them: Rosh HaShanah 29b
In having them Sit in the Succah: Succah 2b, 28a, 28b
In reciting Shema: R. Berachot 20a "ketanim"
Giving a Prohibited Item to a Child
We don't recite Kiddush on Yom Kippur and give the wine to a minor, lest he then drink when he matures: Eruvin 40b
Where the Child's status as a Jew is uncertain: Ketuvot 15b
Lending children money for prohibited interest to educate them about its dangers; one should not do it, lest the child be attracted to the prohibition: Shabbat 149b; Bava Metzia 75a