Red Mages have been in the Final Fantasy games since the very first one.
They are classically a mixture of White Mage, Black Mage, and Warrior; with some abilities from each of them but not nearly as good as any of those classes in their specialties. Sort of a jack-of-all-trades, master of none class. They wear long red capes and large wide-brimmed red hats with white feathers in them and look somewhat "dandified".
In FFXI they had a special support role in groups and were masters of buff/debuff magic.
I have always liked them because they look awesome and are sort of the "wild card" class.
