Abilities in the use of the One Power in specific areas:

Aligning the Matrix

The ability to make metals stronger. (LoC,Ch39)

Arrows of Fire

Lews Therin weaves Fire and Earth into Arrows of Fire, flaming needles that shoot from his fingers. (KoD,Ch19)

Blossoms of Fire

Lews Therin weaves Earth, Air and Fire into Blossoms of Fire, a tall, narrow cylinder of fire that suddenly expands to a disc destroying everything it touches. (KoD,Ch19)

Caressing the Child

The ability to detect the health and condition of a pregnant woman and her fetus. It is a common weave among Wise Ones but unknown to Aes Sedai. (CoT,Ch14)

Cloud Dancing

The ability to control and change the weather. This Talent is cultivated by the Sea Folk Windfinders who call it Weaving of Winds. (ACoS,Ch13) The Salidar Aes Sedai mistakenly do not believe that Windfinders are as good at Cloud Dancing as Aes Sedai. (TPoD,Ch16)

Compulsion

Egwene is concerned that Rand used Compulsion on the Aes Sedai who answer to him. Egwene knows the weave for Compulsion from Moghedien. (CoT,Ch18)
Egwene is disgusted when Lelaine and Maigan suggest altering the Warder bond for Asha'man to make it more like Compulsion.

Deathgate

Lews Therin weaves Spirit with Fire for a gateway then adds Earth to make it travel along the ground for a Deathgate. (KoD,Ch19)

Delving

Related to Healing, this is the use of the One Power to examine a person for illness or injury. After Gitara collapses, Tamra Delves her with Air, Water and Spirit. (NS,Ch2)

Dreaming

Having dreams that foretell future events. This is a rare Talent that is not connected to the One Power or the ability to channel (ACoS,Ch10). It is closely linked with Foretelling. (TGH,Ch12) Unlike other prophetic tools, Dreams portray what will probably happen. They can be difficult to interpret. Known Dreamers - Egwene al'Vere, Amys, Bair, Melaine. See Prophecies for specific Dreams. See also Tel'aran'rhiod.

Dreamwalking

The ability to enter Tel'aran'rhiod from one's sleep. This is a rare Talent that is not connected to the One Power or the ability to channel. (ACoS,Ch10) The Wise Ones believe that male dreamwalkers are extremely rare. (ACoS,Ch10) Known dreamwalkers - Egwene al'Vere, Amys, Bair, Melaine. See also Tel'aran'rhiod.

Earth Singing

The ability to control movements of the earth, for example, preventing or causing earthquakes or avalanches. (Lord of Chaos,Glossary)

Finder

A weave of Spirit applied to an object that gives the weaver a sense of direction and distance to the object, much like the Warder bond. It will last for weeks on cloth or leather and indefinitely on metal. Elayne weaves a Finder on Samwil Hark's when she sends him to follow Doilin Mellar. (KoD,Ch16) Moiraine weaves a Finder on the three coins she gives to Rand, Mat and Perrin. (TEotW,Ch2)

Folded Light

The ability to bend light around oneself rendering the person invisible. This weave is closely related to Illusion. Rand channels Fire and Air to weave Folded Light so he can search for his attackers unseen. (TPoD,Ch29)

Foretelling

The ability to see part of the Pattern. Very rare. It is closely linked with Dreaming. (TGH,Ch12) Elaida a'Roihan, Gitara Moroso and Nicola Treehill have the Talent. Although always true, Foretellings are often very difficult to interpret. See Prophecies, Visions & Foretellings for specific Foretellings.

Healing

The ability to use the One Power to cure injuries and illness. A relatively common Talent, it is the specialty of the Yellow Ajah. Conventional Healing uses Spirit, Wind, and Water, but Nynaeve and the Asha'man have discovered a more advanced method using all five Powers. (ACoS,Ch24)
Beonin teaches Elaida the new weave for Healing. (KoD,Ch2)
Romanda is chagrined that some of the novices are better at the new weave for Healing than she is. (KoD,Ch23)

Illusion

Using the One Power to change one's appearance. In Baerlon, Moiraine uses Illusion to make herself appear as a giant. (TEotW,Ch17) Alanna weaves Illusion from Air and Fire to make herself appear as a giant. (LoC,Ch10) Merana and her party weave Illusion to intimidate Rand. From Asmodean's teaching he recognizes it as the Mirror of Mists. (LoC,Ch49)

Inverting

Weaves can be inverted so that only the person who created the weave can see it. Lanfear inverted the shield on Asmodean. (TFoH,Ch3)

Keeping

A weave that protects a perishable object and keeps it permanently fresh. (WH,Ch12)
The food in the Salidar Aes Sedai camp is spoiling despite the weave of Keeping that was used on it. (CoT,Ch17)
Beonin teaches Elaida the new weave for Keeping. (KoD,Ch2)
The weaves of Keeping are failing in the Salidar Aes Sedai camp. (KoD,Ch23)
Elaida allowed the new weave of Keeping to be broadly taught in the White Tower. (KoD,Ch25)

Milking Tears

Unknown (LoC,Ch39)

Mirror of Mists, or Mask of Mirrors

The ability to alter one's appearance or make oneself invisible. Aes Sedai know a simple version called Illusion. Moiraine knows invisibility. Asmodean taught the Mirror of Mists to Rand. (LoC,Ch49) Moiraine renders her party invisible when they make camp in the Blight (TEotW,Ch48). Sammael and Graendal disguise themselves with the Mask of Mirrors when they visit Sevanna (ACoS,Ch20). Rand disguises himself with the Mask of Mirrors when he and Min go to the Royal Palace to pick up Nynaeve. (WH,Ch11).
A weave can also be used to alter one's voice. (Interviews).

Reading Residues

All channelers can detect the residue of weavings, but some have this ability so refined that they can read and duplicate a weaving as much as two days after it has dissipated. Aviendha has this Talent. (TPoD,Ch2)
There are weaves that a woman can use to detect the resonance of the residue of saidin. The weaves do not detect saidin weaves directly. (Tor Website Q&A)

Reading Ter'angreal

Channelers with this Talent can examine a ter'angreal and determine its use. Aviendha is the only known person with this Talent. (KoD,Ch15)

Seeing Ta'veren

The ability to sense that someone is ta'veren. Rare. Siuan Sanche , Logain and Nicola Treehill have this talent. Alar, the Eldest Elder of Stedding Tsofu, also can sense ta'veren.

Skimming

The ability to open a gateway to a dark dimension (not well defined or understood), move through that dimension, and open another gateway back into the real world in a different location. First mention is TFoH,Ch6. Anyone of sufficient strength and knowledge can Skim. Skimming requires detailed knowledge of the place one is Skimming to. Skimming was not even known as a lost Talent. (ACoS,Ch9)

Spinning Earthfire

Unknown (LoC,Ch39)

Traveling

Opening a gateway directly to another place is called Traveling. It requires that one knows their starting point well. (TFoH,Ch6) The ability to open a gateway directly from one location to another. Anyone of sufficient strength and knowledge can Travel. Traveling requires detailed knowledge of the place one is Traveling from. Gaining sufficient knowledge takes several hours. (ACoS,Ch9) However, when Traveling a very short distance almost no knowledge is needed. (ACoS,Ch41) It is not necessary to face the direction that you want to Travel, but for some it helps. (TPoD,Ch21) Male and female Traveling are very different. Rand describes Traveling as punching a hole from one place to another. On her own, Egwene figures out how to Travel to Tel'aran'rhiod in the flesh by creating a similarity between a place and its image. (LoC,Ch27)

Unweaving

The ability to take apart a One Power weave as opposed to letting it fade naturally. Moiraine undoes her invisibility weave to avoid being traced in the Blight. (TEotW,Ch49) Aviendha and some of the Wise Ones have this ability, but it is unknown to the Aes Sedai. (TPoD,Ch2)

Balefire#

Balefire is an extremely dangerous weapon of the One Power. It actually destroys the thread of existence back into time, the time being proportional to the strength of the beam. Balefire was used in the War of Power destroying entire cities until it was learned that excessive use of balefire could threaten the existence of the entire Pattern.

References (Possible Spoilers)#