What is it?: Parents of the main character being dead.
Worst offenders: Pretty much any anime made after the 1980's... and before as well.
Variants: Variants? I don't know, maybe brother or sister being dead?
Notable exceptions: Only when the parents are the kind that they're so rich they're always travelling for business, which is just another excuse for them to never appear in the story anyway.
What makes it popular: I'm not even sure. Maybe it's been used so much it's become some sort of rule of anime. And because parents are boring, and it makes space for some drama.
Does the hate really worth it?: I think so, since it's unbelievably overused. What kind of universe is it where every teenager must have a dead parent?