Classes of magic:
Black or Unholy Magic: Drawn from Mazoku and their subordinates, often times offensive and destructive in nature.
White or Holy Magic: Drawn from the gods and their subordinates, usually more defensive.
Shamanistic: Magic drawn from nature, nature spirits, or spirits.
Fusion magic: Magic that is fused from two or more forces, often times, two opposite forces.
Auto-magic: Magic that comes from the self.
Chaos magic: Magic that draws from the primordial chaos.
Nature of effects:
Sustained: The spell is sustained until lifted, expired, or broken.
Unsustainable: Magic that expires after the spell is done, i.e. doesn't stay.
Summoning magic: Sustained magic used with the goal summoning a being or thing. Evoking is the same as summoning, invocation is a type of summoning in which the person places an entity in an object or being.
Creation magic: Magic used to create something, i.e. golem, usually sustained magic.
Banishing/Wards: Magic used to banish. Usually, banishings are unsustained, while wards are sustained.
Death magic: Magic used to cause destruction, (Any kind of destruction.) can be sustained or unsustained. Usually, does not last long.
Curse: A curse is used to sustain misfortune on a foe.
Purfication: Magic used to purify an area of something. A majority of the time it is not sustainable.
Dispelling: magic that dispells other spells.
Consencration: Magic designed to make a specific object (and maybe being?) dedicated to the something or someone.
Shielding: Spells that block and shield.
Trap/Trick: Spells that are specifically used in trapping entities and using tricks. These including illusion spells.
Boost: Spells that are to boost a trait or thing in life of the caster or ally. (Flying spells and spells to attract someone to you.) Boost spells are sustained or can boost someone's stats for a short period, teaching the skills they need, and disappear.
Healing: Magic specifically made for recovery. It is usually unsustained unless for a prolonged period.
Bindings: Sustained magic that bounds something or someone to an object, place, or thing.
Dream [otherworld] magic: Spells geared specifically for dreaming.
Shapeshifting: The art of turning into other things or beings, usally an animal. Shapeshifting, is almost always sustained.
Drain: Magic designed specifically to take life force or other energies from a target or targets to heal the caster with. It is uncommon for it to be sustained for long periods and is almost always offensive.
This is all I can think of now. I'll add more with suggestions.