For a good person [Adam Kasher]: Shabbat 105b, Moed Katan 25a
For one who is present at anyone's moment of death: Shabbat 105b, Moed Katan 25a
For a grandchild: Moed Katan 20b
Tearing the clothing of a Minor who is a Relative, to induce others to mourn for the deceased: Moed Katan 14b, 26b
Tearing clothing for News of a relative's Recent Death where the news came on Shabbat and after Shabbat it will be in the category of "Distant News": Moed Katan 20b
Tearing for in-laws, in respect for one's wife: Moed Katan 26b
Tearing clothing as long as one is involved in eulogizing the deceased: Moed Katan 25a
Tearing Clothes in Grief
Tearing for bad news, and repairing such a tear: Moed Katan 26a
The "bad news" tearing is if affects the majority of the populace: Moed Katan 26a