Yet before continuing I must add that, in all of its incalculable forms, magic does have one great commonality: though ancient beyond thought and twice as mysterious, it does have rules. All things have rules.
1. Earth Magic: The deep magic of the land itself and, incidentally, my personal favorite. Earth Magic generally affords the user with a special sixth sense attuning her/him with the land itself – thus telling them when the land is poisoned or something unnatural is occurring. Typically the magic of Druids, rangers, and herbalists, Earth Magic may also grant a special affinity with animals (such as the gift of understanding their tongue). Simply put, it is the magic of, and thus draws power from and affords the user some control over, nature itself and is benevolent almost as a rule.
2. Blood Magic: A typically foul branch of sorcery, Blood Magic is near always of the Dark, or forbidden, Arts and usually involves mages using ritual (human) sacrifice in an attempt to gather a vast amount of power quickly. As such, its practitioners are 99% of the time ambitious fiends who are willing to advance themselves and their interests via the torment of others (their victims). Put plainly, typical blood-mages draw their power from pain and death (and natural power inherent in blood) – doing so because it is quick and easy and often provides them with a sadistic kind of pleasure.
The dark twin and near opposite of Earth Magic, one can generally tell the rare benevolent user of Blood Magic apart from the rest by the fact that they often use their own blood or, if necessary, blood from a painlessly sacrificed creature.
3. Time Magic: Usually Time Magic is akin to non sci-fi time travel with a few extra quirks thrown in, when it is used at all. (See the White Chronicle entry on my The Role and Proper Usage of Magic Thingamajigs page to get my fuller take on Time Magic because, interestingly and like in sci-fi, Time Magic in Fantasy is typically employed through the medium of a time-travel device.)
4. Ritual/Summoning Magic: Neither good nor evil at face value, Ritual/Summoning Magic typically is the branch employed when a mage wishes to call something from, or effect another via, another Plane of Existence. Think summing Demons and/or Elementals in the first instance, and performing a healing or sacrificial ritual that involves Other Powers in the second.
A cousin to virtually all forms of magery, it also covers the term Spirit Magic (due to the Spirit World being another Plane of Existence).
5. Soul Magic: A branch that is offhand neither good nor evil, though its most common form is of the latter – i.e. Necromancy. Anyway, simply put, Soul Magic is a form or sorcery that either draws powers from one's Soul, in some way affects its nature, summons it, or banishes it. Soul Magic is, as a rule, rare and I seldom encounter it in Fantasy.
It is a cousin of Blood Magic, as a person's blood may often be a used as a tool to manipulate their Soul.
6. Divine Magic: For good or ill and in countless different forms and ways, calling upon the power of deities.
7. Rune Magic: Complex as a rule and thus subject to any number of rules, the overriding law of this form of magery is that it is drawn, or in some other way dependent upon, the power of mystical runes/glyphs.
8. Mind Magic: A very common form, Mind Magic at its purest is drawn solely from the power of the user's mind and force of will. One could call it psychic if one so wished.
It all really just boils down to the Mind over Matter concept, in my opinion, though it often is drawn from a combination of the user's mental and physical strength.
9. Physical Magic: A very common form, Physical Magic at its purest is draws solely upon the user's physical strength/energy. Once the mage completely runs out of said energy, she/he dies.
The opposite of Mind Magic, the two are still often mixed together in the manner I described above.
I can hear you all saying, "But what about High Magic?" After all, it is a classical Fantasy term used to refer to types of magery. The keyword here is "types," for High Magic is really just a classification given to the grander and more powerful forms of magery, and therefore is not a branch of magic in and of itself.
The same principle applies to Black/Dark Magic and White/Light Magic; the names generally do not refer to a specific type of sorcery so much as the morality or lack thereof behind its use.