Magic is a foreign element to Abode, brought by the High Ones. The use of magic is possible only for elves. The trolls with whom they share their exile have no magic, and humans are only capable of exhibiting magic through the use of technology.
Every elf has the potential for magic within, but some never show signs of it. In some tribes, such as the folk of Sorrow's End, the most basic powers, such as Sending, have atrophied. Theoretically, any elf could do any magic, but in fact, this is impossible. Certain elves have inherent powers, such as healing, plant-shaping, rock-shaping, flesh-shaping, and have no ability with other powers. Sometimes it takes a traumatic incident to bring these powers to the fore in an elf; other times an elf develops the powers from long disciplined practice. No elf -- even among the High Ones -- has held the ability to use all types of magic since their exile on the World of Two Moons. 
Known users: Most elves.
Sending is a form of telepathic communication between elves. One cannot lie in sending, and it is difficult to hide your emotions in it; they are as much linked to the message as the words themselves. One can respond to Sending even when unconscious, though the coherency of the reply is unknown.  The distance that one can Send varies on an individual basis.
Sending is intrinsic to all elves. While some tribes may have lost the knowledge of how to Send, there has been no sign of any elf or tribe that cannot learn to Send. Shenshen, for example, was never able to Send for hundreds of years while living in the Sun Village, but she developed the ability shortly after being exposed to the Palace's magic for the first time. She was also able to receive and understand her sister Leetah's Sending before she herself was capable of doing so.
Richard Pini notes in The Big Elfquest Gatherum (article "Recognition, or How Loud is your Lizard?") that even an elf who has never experienced Sending can still make telepathic contact with another elf during Recognition.
This power detaches one's essence from one's body. Once the user is out of his or her body, the elf's spirit can communicate with others over far greater distances than by Sending and can observe distant events much more clearly than through clairvoyance / "parting the mist". When one elf's spirit touches another's, the two can communicate and exchange a great deal of memories in just a brief moment. When in the astral plane, an elf's spirit can be caught through the use of Mind-Snare; at this point, their body is left comatose. If they do not return to their body, they will slowly waste away and eventually die. 
Mind-Stun / HypnosisEdit
Known users: Rayek
Upon making eye contact with another living creature, the user can stun them into a state of no volition. The victim will stand shocked and be unable to defend himself, paying no attention to his surroundings and being unable to attack. They also become prone to suggestion at this point: Rayek, during his time at the Sun Village, uses this skill to tame the Zwoots. It also may have been used initially by the Blue Mountain elves to convince their humans to attend them. 
That said, the victim can only be coerced to a point; they will not follow orders that demand they go against their intrinsic morals or instincts.
Known users: Winnowill
This brutal tactic allows one elf's spirit to capture another's and hold it, adding the captured elf's power to the captor's own. Winnowill once captured Savah's spirit for an extended period, and she later tried to capture Sunspot's. She stated an intention to use Sunspot's spirit to lure Timmain to her ("through her trust and faith in him"), possibly indicating that the user of a Mind-Snare can impersonate their captured victim in Sending.
Known users: Venka
The user can prevent another elf from Sending or from using other magical abilities, such as when Venka cut off her father Rayek's gliding ability in mid-flight and caused him to crash to the ground. A user of this ability can also prevent telepathic "spying", as when a teenaged Venka would catch Winnowill "snooping around" the Wolfriders from a distance and "shoo her away". Being blocked in this way is often portrayed as painful to the elf attempting to Send or otherwise use magic.
Healing is one of the rarer magics, though it is in no danger of becoming extinct. A healer can fix another elf's wounds through their own force of will: at points, it has even been shown that they can heal humans.
Healers can also affect the mind, though their abilities in this respect seem limited. Though Leetah is capable of partially alleviating the symptoms of Two-Edge's madness, the cause (his underlying trauma from his childhood abuse) still remains. Leetah once tried to heal Winnowill but was interrupted, and Winnowill later stated that the partial healing had only caused more damage than it healed.
Healing requires physical contact in order to work, except in cases where an extraordinary amount of healing energy is created, as when Leetah and Mender joined their energies with those of the Palace to heal many of their nearby tribemates.
Shielding can be used both mentally, to protect a user against Blacksending, and physically, to protect themselves against an attack. Using this ability can create a thin, transparent shield, almost always curved and relatively small in size.
Known users: Winnowill Anti-healing is the inversion of healing: instead of mending wounds, it creates them. Any healer can use anti-healing, but only healers are capable of using the ability. Anti-healing can cause wounds of various sizes, but has the same restrictions as healing: it requires the user and the victim to be in physical contact in order to work.
In addition to harming its victim, anti-healing can be used to put them into a trance. 
Originally, all Coneheads were shapeshifters, capable of changing their forms as they willed: it was through this that, when they discovered Abode, they changed their bodies into elves. Now, self-shaping is one of the rarest abilities. Self-shaping is essentially just shapeshifting, into whatever the user desires. There appears to be no upper size limit or restrictions as to what they can turn into.
When self-shaping, the elf is biologically identical to the animal or person that they have changed into, except that their original mass is conserved. While in this other form, they can breed and produce viable offspring: it is from one such mating, between Timmain and a wolf, that the Wolfriders were born. Self-shaping, however, can be dangerous. The longer the amount of time spent in another form, the more likely that the shapeshifter will forget their original form - and with it, forget how to turn back into it.
Known users: Winnowill, Two-Edge Flesh-shaping is essentially the same as self-shaping, except directed outwards. It is an ability restricted to healers, but is a very advanced application of healing magic that few healers develop. Rain, the Wolfriders' healer, is only known to have used it to close up Woodhue's eye socket after the eye was gouged out by humans; he did not have the skill necessary to regenerate the eye itself.
Flesh-shaping is used frequently among both tribes of Wavedancers, for mere aesthetic purposes such as adding fins and changing the shape of their ears as much as for practical ones, such as adding gills and fishtails. It is used less frequently among the Gliders, with Tyldak being the only example.
Healers have been known to change Wolfriders' biology at a fundamental level, changing a wolf-blooded, mortal elf into a pure-blooded, immortal elf. Winnowill did so to Windkin in infancy, and Leetah did this for Skywise at his request.
Known users: Goodtree, Redlance, Kaslen This power manipulates plants to shape them to the user's needs. This trait seems has been fairly common throughout the history of the Wolfriders, and both Lord Voll and Winnowill have mentioned Gliders with the ability (although they have not been shown). The Sun Villagers were unaware of this ability until Redlance's power surfaced. Wolfriders and Gliders call the power Tree-shaping, but Plains Elves (Plainsrunners) use it to alter bushes and other small plants. . 
Known users: Ahdri, Door, Ekuar, Osek, Mekda, Aurek and many other Gliders, Longfin. Rockshaping is the manipulation of stone, in order to shape it to the wielder's wishes. Like plant-shaping, rock-shaping is a rare talent among the elves. It never appeared among the Wolfriders, probably because they never had need for it in the forest.  Rockshaping can be used to detect faults and unnatural changes to rocks, such as doors or interiors.
Known users: Ahdri, Alekah The ability to shape metal, including gold, "bright-metal", and others. Ahdri discovers this ability when she accidently fixes a gold piece she was working on. Her ancestor, Alekah (granddaughter of Savah) also had this ability, and she used it to shape the golden sun symbol above the Bridge of Destiny. Some of the Gliders possessed this skill as well, according to the roleplaying games, which state "[metal-shaping is] used by the Gliders to make the weapons with which they supply the human tribes dependent on them."
Coral-ShapingEditKnown users: Tentus, Snakeskin Coralshaping is the shaping of coral, usually into some form of a habitat or barrier. It can be presumed to be a magic unique to the Wavedancers, as it has not appeared in any other tribe of elves.
Coral is neither rock nor plant, and yet is still shown to be shaped by both tribes of Wavedancers. Since coral is a living organism, and an animal to boot, it's been placed under flesh-shaping. With that said, neither Tentus or Snakeskin have shown any signs of being capable of 'traditional' flesh-shaping.
This is the ability to ignite an object, though its difficulty greatly increases depending on how flammable it is. Unlike other magics, firestarting seems intrinsically incompatible with Abode: the first firestarters amongst the Wolfriders rapidly decreased in strength, and one of the attempts at using their fire-starting by the Firstborn resulted in the pool of bad magic that caused Madcoil's eventual birth. Zarhan, in Rahnee's generation, was the last confirmed firestarter, and the ability appears to have died out since then.
That said, other early generations of elves appeared to have been capable of using it, at least somewhat successfully according to Lord Voll's memories of the first days of the Gliders. 
Known users: Savah
Savah's ability has never been officially named, but she is shown at several points to light the lamps of the Sun Village without any physical movement. Similarly, the light behind her throne -- which fades upon her being captured on the Astral Plane -- has been accredited to this power. Her ability could be the only example of modern firestarting, or a completely different magic.
Known users: Rayek, Aurek This power allows oneself to lift an object, or another person through sheer force of mind. There doesn't appear to be an upper size limit, as long as the practicioner has enough mental strength to lift the object. It is implied that the Palace moves through this method.
A subsect of levitation, this power (named Gliding by the residents of the Blue Mountain) allows one to lift themselves into the air. This ability uses the user's force of mind to propel themselves, not air currents. Gliders are slower than creatures that fly through more traditional means, but do not appear to tire easily from gliding: they can stay in the air despite ample distraction, as is shown by Aroree.
This is an ability intrinsic to most elves: only a small portion of the population does not have it, though the strength varies from individual. Magic feeling is the ability to sense if a nearby object or place has magical properties, was created through magical means or if a great working of magic was done at that site. 
Known users: Finder This ability allows the user to attempt to find something he's familiar with and needs, within 300 yards of where he is standing. However, it can actually be used to find anything the user is familiar with, including types of rocks, a lost friend, or a lost ornament.
Known users: Rayek