Slavery is abhorred and strictly forbidden on the Westerosi mainland, likely due to the Faith of the Seven brought by the Andals six thousand years ago. The Faith is the dominant religion in the Seven Kingdoms and it forbids the practice of slavery.
Aenar Targaryen brought slaves to Dragonstone when his family moved from Valyria in anticipation of the Doom, although slavery in the former Valyrian outposts in the narrow sea appears to have been abolished or phased out sometime between the Doom and Aegon's Conquest, or at the very latest, shortly after the Conquest.
The ironborn of the Iron Islands keep thralls and salt wives. Neither are slaves in the literal sense, but are subject to forced labor and low status, and are not far removed from enslavement. Their children, however, are considered free if they are drowned to the Drowned God.
However, the illegal practice does take place in Westeros sometimes. Ser Jorah Mormont once sold a few poachers to some Tyroshi slavers and had to flee to the Free Cities when his crime was discovered by Lord Eddard Stark, who condemned Jorah to death for his crime. It is said that Cersei Lannister had the mother of King Robert I Baratheon's bastard twins sold to a passing slaver, presumably because she could not bear such an affront to her pride that close to home.
In the Free Cities, well spoken and gently born slaves are prized. They become tutors, scribes, bed slaves, healers, and priests.
- In Pentos, slavery is forbidden by law, as part of the terms imposed by the Braavosi on Pentos a hundred years ago. However, in a city where wealth equals power, many rich magisters flout such laws and bronze-collared slaves are common on their estates. One such case is Illyrio Mopatis, who has a finger in the slave trade, and maybe a whole hand.
- Lys has a high slave population. Slaves are used for labor too harsh for Lysene hands, trained to act as guards and soldiers, and even posed for various performances. Lys is well known for its pleasure houses, training slaves in the arts of love and selling them as concubines and bed-slaves.
- In Volantis, due to the relative proximity to Slaver's Bay, there is a thriving slave market. There are five slaves for every free man. Slaves are always tattooed on the face, which prevents escaping on the constant flow of ships. Such tattoos are often designed to reveal the slave's role. A fool might be patterned in tattooed motley from neck to scalp.
- Qohor's city guard is comprised solely of Unsullied eunuch slave soldiers. However, much like in Pentos slaves can be bought by powerful men who flout the laws.
- Myr is a hub of trade in slaves.
- Tyrosh deals extensively in slaves and Tyroshi slavers are known to be especially aggressive. They even sail north beyond the Wall, in search of wildlings to enslave.
- Braavos is an exception among the Free Cities. Descended from escaped slaves, the Braavosi do not permit slavery and they do not trade with Slaver's Bay.
Yunkai, Meereen, and Astapor are the great slaver cities of Slaver's Bay. For centuries, they have been the linchpins of the slave trade, the place where Dothraki khals and the corsairs of the Basilisk Isles sell their captives and the rest of the world comes to buy.
The Dothraki make slaves by enslaving conquered peoples and selling them, often to the Ghiscari who train them. Dothraki keep slaves from many lands, notably in Vaes Dothrak, which was built by slaves, where they serve the dosh khaleen. Dothraki also sell their own kind, and when khalasars battle the defeated Dothraki are enslaved. 
The Qartheen trade in slaves.
At the beginning of its rise to power Valyria had watched the Ghiscari grow rich and powerful off the backs of conquered peoples. After the fall of Ghis the self-styled freehold wanted its turn, seeking to emulate the success that slavery had brought to Ghis. The Valyrian Freehold made extensive use of thousands of slaves from a hundred different nations from throughout Essos.
In the mines underneath the Fourteen Flames "only the worst" slaves toiled, burned, and died to find gold and silver. Slave revolts were common in the mines, but the Valyrians were strong in sorcery and able to put them down. When there was war, the Valyrians took thousands of slaves, and when there was peace they bred them.
It is said the first Faceless Man existed in Valyria. There he brought death to the slaves who lived horrid lives toiling in the heat of the Fourteen Flames, praying for an end. He came to realize that the many gods they prayed to were one god, and that he was an instrument of the gods.
The city of Gogossos on the Isle of Tears outlived the Doom of Valyria and waxed rich and powerful during the Century of Blood, some calling it the "Tenth Free City", thanks to slavery and sorcery. Its slave markets became as notorious as those of the cities of Slaver's Bay. However, seventy seven years after the Doom a terrible plague, the Red Death, emerged from the slave pens of the city and swept across the Isle of Tears and then the rest of the Basilisk Isles.
A Game of Thrones
After Khal Drogo's defeat of Khal Ogo and the Lamb Men, Ser Jorah Mormont advises him to make for Meereen. The city had a plague the previous year so the brothels are paying double for healthy young girls and triple for boys under ten. Jorah tells Daenerys Targaryen that if enough enslaved children survive the journey the gold earned from their sale will buy them all the ships they need to sail for Westeros. Before her dragons are born Daenerys frees the slaves of what is left to her of Drogo's khalasar.
A Clash of Kings
Before giving her khalasar the order to enter the red waste, Daenerys contemplates heading downriver with her ragged band to the ports of Meereen, Yunkai, and Astapor, but Rakharo warns her that Khal Pono's khalasar had ridden that way, driving thousands of captives before them to sell in the fleshmarts of Slaver's Bay.
A Storm of Swords
Daenerys frees slaves at Astapor, Yunkai, and Meereen. She fills the ranks of her army with the slaves she freed, people who are completely loyal to her and who have no aspirations beyond protecting their newly obtained freedom.
A Feast for Crows
Euron Greyjoy mentioned that the price of slaves is rising since the fall of Astapor and Meereen. After the taking of the Shields, Euron plans to sell his captives as slaves in Lys and Volantis which will give the Iron Fleet sufficient gold to buy provisions. Victarion Greyjoy is disturbed by this as it is not the Old Way.
A Dance with Dragons
According to Qavo Nogarys, a customs officer Selhorys, the actions of Daenerys have smashed the slave trade which Volantis and Qarth rely on, making the dragon queen enemies behind the Black Wall and beyond.
As part of the peace between the Wise Masters and Daenerys Targaryen, Queen of Meereen, slavery is prohibited within the walls of Meereen but Yunkai is free to trade in slaves unmolested. The Yunkish lords besieging the city set up a slave market within sight of its walls.
Notable former slaves
- Strong Belwas
- Grey Worm
- Stalwart Shield
- Symon Stripeback
- Tumco Lho
- Red Lamb
- Tyrion Lannister
- Ser Jorah Mormont
- widow of the waterfront
- the freedmen that make up the Mother's Men
- Melisandre - (free status is questionable: unclear if she is a Slave of R'hllor/free/gone rogue/escaped)
- Marq Mandrake
A man should be able to do as he likes with his own chattel. 
Lot ninety-seven … A pair of dwarfs, well trained for your amusement.
My queen, there have been no slaves in the Seven Kingdoms for thousands of years. The old gods and the new alike hold slavery to be an abomination. Evil. If you should land in Westeros at the head of a slave army, many good men will oppose you for no other reason than that. You will do great harm to your cause, and to the honor of your House. —[Barristan Selmy
No man wants to be owned
Slaves perished by the score, but their masters did not care. Red gold and yellow gold and silver were reckoned to be more precious than the lives of slaves, for slaves were cheap in the old Freehold. 
—thoughts of Victarion Greyjoy
There have been no slaves in the Seven Kingdoms for thousands of years. The old gods and the new alike hold slavery to be an abomination. Evil. If you should land in Westeros at the head of a slave army, many good men will oppose you for no other reason than that. You will do great harm to your cause, and to the honour of your House.
There was never a slave who did not choose to be a slave. Their choice may be between bondage and death, but the choice is always there. —thoughts of Tyrion Lannister
This arrogant child has taken it upon herself to smash the slave trade, but that traffic was never confined to Slaver's Bay. It was part of the sea of trade that spanned the world, and the dragon queen has clouded the water. 
Xaro: We curse the rain when it falls upon our heads, yet without it we should starve. The world needs rain ... and slaves. You make a face, but it is true. Consider Qarth. In art, music, magic, trade, all that makes us more than beasts, Qarth sits above the rest of mankind as you sit at the summit of this pyramid ... but below, in place of bricks, the magnificence that is the Queen of Cities rests upon the backs of slaves. Ask yourself, if all men must grub in the dirt for food, how shall any man lift his eyes to contemplate the stars? If each of us must break his back to build a hovel, who shall raise the temples to glorify the gods? For some men to be great, others must be enslaved.
Daenerys: Slavery is not the same as rain. I have been rained on and I have been sold. It is not the same. No man wants to be owned. 
Yezzan's slaves ate better than many peasants back in the Seven Kingdoms and were less likely to starve to death come winter. Slaves were chattel, aye. They could be bought and sold, whipped and branded, used for carnal pleasure of their owners, bred to make more slaves. In that sense they were no more than dogs or horses. But most lords treated their dogs and horses well enough. Proud men might shout that they would sooner die free than live as slaves, but pride was cheap. When the steel struck the flint, such men were as rare as dragon's teeth; elsewise the world would not have been so full of slaves. —thoughts of Tyrion Lannister
—Tyrion Lannister, during his time as a slave
You could breed the two of them, get good coin for the whelps.
- A Storm of Swords, Chapter 23, Daenerys II.
- The World of Ice & Fire, The Reign of the Dragons: The Conquest.
- Fire & Blood, Aegon's Conquest.
- A Game of Thrones, Chapter 35, Eddard IX.
- A Dance with Dragons, Chapter 66, Tyrion XII.
- A Storm of Swords, Chapter 71, Daenerys VI.
- A Dance with Dragons, Chapter 1, Tyrion I.
- A Game of Thrones, Chapter 3, Daenerys I.
- A Clash of Kings, Prologue.
- A Clash of Kings, Chapter 63, Daenerys V.
- The World of Ice & Fire, The Free Cities: The Quarrelsome Daughters: Myr, Lys, and Tyrosh.
- The World of Ice & Fire, The Free Cities: Braavos.
- A Storm of Swords, Chapter 42, Daenerys IV.
- A Dance with Dragons, Chapter 30, Daenerys V.
- A Feast for Crows, Chapter 22, Arya II.
- A Game of Thrones, Chapter 61, Daenerys VII.
- A Clash of Kings, Chapter 48, Daenerys IV.
- A Clash of Kings, Chapter 12, Daenerys I.
- A Feast for Crows, Chapter 29, The Reaver.
- A Dance with Dragons, Chapter 31, Melisandre I.
- A Dance with Dragons, Chapter 56, The Iron Suitor.
- A Dance with Dragons, Chapter 22, Tyrion VI.
- A Dance with Dragons, Chapter 16, Daenerys III.