Early kal'dorei civilization was defined by direct manipulation of magic drawn from the Well of Eternity to create and sustain their society. The constant use of the well attracted attention from Sargeras and the Burning Legion, and their coming resulted in a massive war known as the War of the Ancients. The war had grave consequences, for even though the combined might of Azeroth's mortal races were victorious, the supercontinent of Kalimdor was shattered, and a swirling, raging miasma of seastorms flowed into the vacant area where the Well of Eternity use to reside. This Great Sundering caused the Well's waters to be permeated into the atmosphere and spread magic all over the world.
This event convinced the majority of night elves to reject arcane magic and embrace Malfurion Stormrage's call for druidism. Many of the Highborne refused this lifestyle, and left in self-imposed exile to Lordaeron where they eventually founded their kingdom of Quel'Thalas and became the High Elves. When their kingdom came under siege by the trolls of Zul'Aman the high elves agreed to teach one hundred humans the arts of magic in exchange for military aid from the human nation of Arathor. From these two races, the arcane arts have spread to various races all over Azeroth.
The most powerful mages came from the city-state of Dalaran, until it was destroyed by Archimonde during the Second Invasion of the Burning Legion. Without Dalaran and thus without a centralized, ruling body of mages, exploration into the arcane arts has largely been experimental and an individualistic endeavor, as the old regulations and standardized teaching methods espoused by the Kirin Tor - for the most part - do not apply any longer. There is much more emphasis between the master-apprentice relationship then there is to a student-curriculum relationship. There have been both benefits and drawbacks to this. With a general nonexistence of rules the arcane arts have enjoyed a great degree of advancement during the events of World of Warcraft. However, without the authority of the Kirin Tor to fear, the number of warlocks has grown disturbingly high. Many are former mages, and most live openly and declare their study into the forbidden arts publically.
Most of the remaining mages are Human. This is mostly due to the fact that Dalaran was essentially a human nation, and naturally it culled a great majority of its members from humanity. Humans are also the most populous out of all races who study the arcane arts.
When the Quel'dorei trained the first one hundred batch of humans in the most rudimentary of arcana, they were surprised to find the young race had great natural affinity. The sheer, raw power they could summon up even surpassed what high elven casters were capable of mustering, but they lacked control. This trait became what forever characterized the typical style and approach of human mages. Most human mages prefer using fire and arcane spells, as they allow for the caster to dish out salvos of raging energy, which become bigger, powerful and more varied streams as the mage gains experience. However, humans still find it difficult to concentrate and focus their attacks for more precise and subtle effects. For example, while a human mage might find incinerating a cadre of gnolls child's play, lighting the tip of a candle or precisely bombarding a target without harming those around the target may be difficult.
Elven mages tend to have more control over magic than other races. Magic is not just a craft to them, it is the way of life. Having an average lifespan of 350 affords several advantages, including plenty of time to study, hone and discover all manner of spells and different ways of applying them. As a result elves are extremely flexible casters, and can handle themselves in all manner of situations. The long-lived casters are also famed for their concentration, precision and control. Because of this many high elves prefer using frost spells, which rewards accuracy and timing. Frost spells are also highly flexible, being equally useful defensive and offensively, manifesting in various forms such as attacks, armors and cages. Blood elves, upon their self-proclaimed rebirth as a new race, have since embraced fire as their mainstay tree of study.
Because of the aforementioned ability to experiment and tweak their spells throughout their long lifetimes, high elves are much more knowledgeable of magic than mages of other races, and often possess exclusive knowledge on secret and obscure arcana - sometimes, even forbidden and dangerous. They take no humility in constantly reminding other races of this fact.
In a community as eccentric as mages, for other mages to regard gnomish mages as outlandish is really a statement. Gnome mages are characterized by their bizarre and bold (some would say 'whimsically suicidal') probing into just how many things they can get their spells to do. The insatiable curiosity of gnomes is legendary, and all gnomes of all walks of life tinker. Gnomes as a race hold no general preference for any particular tree of magic or school of thought, but all are highly individualistic, and their idiosyncratic spells are evidence. Gnomes have the most creative spell repertoire of all the practicing races by far, and home-made gnomish spells either end up as fabulous successes or extremely dangerous failures.
Forsaken mages are mostly fallen former Human mages; they might as well be affected by their proximity to Dalaran, ancient minions of Archimonde who could roam the ruins of the fallen city and understand the complex science of magic.
Many may wonder how a race performing primitive rituals based around a spiritual religion could wield the arts of the Arcane, yet the recent alliance between the Darkspear Tribe and the Horde showed that the trolls are quite a perceptive race willing to learn new ways if it is for the best of the tribe, much like the Humans back in their primitive days. With the Arcane arts once being exclusively Elven and Human with the Mages of Quel'thalas and the Kirin'Tor of Dalaran, the fall of these organizations during the third war, resulted in many scattered Mages across Azeroth searching for a place to settle. And it is not very unlikely that the Trolls might have adapted their arcane knowledge from these scavengers, as well as from their recent allies the Forsaken, who still as the undead possess knowledge of the Arcane Arts.
Familiars are a valuable addition to a mage's skills. They allow a mage to be more aware of her surroundings and to perform minor espionage and other tasks. However, they can also bring danger - if the familiar is killed, the mage is in trouble. Some magi eschew familiars in favor of focusing more on their magic, channeling energy they would be spending on their familiars into other endeavors. The Kirin Tor, in particular, develops numerous other studies that its members can pursue.