Hate

Good vs. Evil Hate
Angels  Archangels	Devils  Arch Devils
Genies  Master Genies	Efreetii  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-Efreet 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.

Breath attack of Black Dragons does 150% damage on Titans if they attacked another stack, and Titans are behind it. Even if Titans are allied to Black Dragons, the latter will deal additional damage if they attack their own Titans by mistake.

If in the same army there are creatures hating each other, it doesn't spoil their normal functioning. Hate doesn't affect morale, and 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 faction. It 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 Efreet, aside from those ones to which Efreet are immune). If you have creatures with hate ability, their enemies may still join your army if it is strong enough or if you have appropriate Diplomacy skill. Generally, hate is just a simple damage modifier applied before the attack, and nothing more.