What types of magic has been displayed in A song of Ice and Fire / Game of Thrones Universe?

Question

What types of magic has been displayed in the the A song of Ice and Fire / Game of Thrones Universe?

Answer 1

The ASoIaF Wiki has categorized them pretty well:

• Elemental control: Like the priests of R'hllor, they can control elements like fire(like Melissandre and Thoros).
• Divination: Some people can see the future (like Maegi, see also: greensight)
• Skinchanging: People can 'enter' the mind of animals (and humans) (like Bran, Varamyr)
• Raising the dead: The priests of R'hllor have brought people back from the dead (like Thoros resurrected Beric when the latter was killed by the Hound)*
• Necromancy: Some can raise the dead and make them do their willing (like Qyburn planned to do with Gregor Clegane and those skeleton thingys Bran found North of the Wall)
• Glamouring: Some can change their appearence (like Melissandre)

Also, it would be good to point out that the Citadel claims that there is no magic left in the world. They claim it is just a mythical power.

There was supposed to be magic in Valyria as well, but it is said that it perished along with Valyria.

It is said that they could set dragonglass candles to burning with strange, unpleasantly-bright light. With the obsidian candles, they could see across vast distances, look into a man's mind, and speak with one another though they were half the world apart

--A Feast for Crows, Chapter 45, Samwell.

The most powerful magic is said to be originated from the Shadow Lands.

There are firemages who can conjure ladders from the air that are made of fire and can stand forty feet high. The mage can climb up the ladder, each rung disappearing behind him, leaving nothing but silvery smoke. When he reaches the top, the ladder and he are both gone.

--A Clash of Kings, Chapter 40, Daenerys

Moreover, people believe that the children of the forest used to practice magic.

*This kind of magic might have blood as a requirement; Mirri Maz Duur sacrificed a horse to bring Khal Drogo back from the dead.

Answer 2

There are many kinds of magic in the books and TV series. Here's my list of them. I left out anything I could explain through natural means such as wildfire, which is probably just simple chemistry. I deliberately omitted the act of burning people alive to appease the Lord of Light because I am not convinced that is magic, but could be a mere power play by the Red Woman. Nor am I convinced that what the Faceless Men do is real magic.

Reanimating the dead. (The dead body does the bidding of whomever controls it.)

• The Children

Resurrection. (The dead body becomes their former self.)

• Kissed by Fire
• Home

Converting the dead into wights. (I consider this different than merely reanimating the dead because the wights can be reduced to skeletons and still function, while reanimated dead like Gregor Clegane probably could not function after being skeletonized.)

• Winter is Coming - a dead wildling girl is converted to a wight.
• The Pointy End
• Hardhome

Transforming babies into White Walkers

• Oathkeeper

Teleportation.

• Valar Morghulis
• Valar Dohaeris

Bilocation.

• The Ghost of Harrenhal
• A Man Without Honor
• Valar Morghulis

Hatching dragon eggs.

• Fire and Blood - hatching dragon eggs requires a blood sacrifice

Drinking poison and living

• The North Remembers

Visions (both greensight and seeing events in fire)

• The North Remembers
• The Night Lands
• What is Dead May Never Die
• The Ghost of Harrenhal
• Valar Morghulis
• Dark Wings, Dark Words
• The Climb
• Second Sons
• The Lion and the Rose
• The Red Woman
• Home
• Oathbreaker
• The Door
• The Winds of Winter

Foretelling the future.

• The North Remembers
• Valar Morghulis
• The Climb
• The Wars to Come

Unharmed by fire.

• A Golden Crown (I'm referring to Daenarys, and obviously not her brother who died in this episode.)
• The Book of the Stranger

Warging.

• Dark Wings, Dark Words
• The Rains of Castamere
• The Lion and the Rose
• First of His Name
• The Watchers on the Wall
• Mother's Mercy - When Jon Snow warged into his direwolf, Ghost.
• The Red Woman - When Jon Snow warged into his direwolf, Ghost.
• The Door

Birthing shadow demon assassins.

• Garden of Bones

Shadow demon assassination.

• The Ghost of Harrenhal

Protective cave against Wights

• The Children

Glamouring

• The Red Woman

Being saved from becoming a wight

• Blood of My Blood

This list goes only through the sixth season. (More to come!)