Hate

Good vs. Evil Hate
Angels  Archangels	Devils  Arch Devils
Genies  Master Genies	Efreeti  Efreet Sultans
Titans	Black Dragons
Effect: +50% Damage
Elemental Damage Bonus
Air Elementals  Storm Elementals	Earth Elementals  Magma Elementals
Water Elementals  Ice Elementals	Fire Elementals  Energy Elementals
Effect: +100% Damage

Hate is a special ability of creatures, which causes attacking unit to "burn with anger" and deal 50% more base damage (see damage calculation) to a creature type it hates.

Angels-Devils and Genies-Efreeti rivalries involve both basic and upgraded versions of creatures. However, Giants and Red Dragons do not hate anyone. Only Titans and Black Dragons hate each other.

Hate doesn't affect morale if creatures hating each other are in the same army (Devils/Archdevils will even get +1 morale if they are alongside Angels/Archangels - while there won't be morale bonus for all troops from the same town), and doesn't prevent units from spreading their magic abilities on hated allies (i.e Archangels may resurrect Devils and Archdevils, and Master Genies may cast spells on any type of Efreeti, aside from those ones to which Efreeti are immune). More precisely, hate is just a simple damage modifier applied before the attack, and nothing more.