While the set items themselves are without any stat bonuses (with the exception of the Boots, which always have +1 MP) they provide special bonuses to the relevant classes spells, such as removing the need for Line of Sight or Linear constrictions.
It should be noted that the +Damage from class set pieces acts as normal +Damage (though it only affects the relevant spells) and does not affect the spell's base damage.
Any class can actually wear another classes set pieces, though will obviously gain no bonus to their spells. All pieces of a class set will take on the colors of the character wearing them.
Lastly pieces of a class set cannot be maged.
Below is a list of the sets specific to each class.