Incest is defined as a relationship between two persons commonly regarded as too closely related to marry. 
Incest in Westeros
Incest in the Seven Kingdoms
The two main religions practised in the Seven Kingdoms, the Faith of the Seven and the old gods, consider incest to be a vile sin. However, according to their marriage customs, it is acceptable and in fact quite common among the nobility for cousins to wed. Examples include Tywin and Joanna Lannister (first cousins), Paxter Redwyne and Mina Tyrell (first cousins), Viserys I Targaryen and Aemma Arryn (first cousins), Jocelyn Baratheon and Aemon Targaryen (first cousins once removed), and Rickard and Lyarra Stark (first cousins once removed). The exact degree of relations are unknown in the marriages of Jon and Rowena Arryn, Shella and Walter Whent, Benfrey and Jyanna Frey, and Alys and Jared Frey. Further, a marriage has been proposed between Robert Arryn and Sansa Stark (first cousins), to which the degree of common ancestry was not an objection.
The Westerosi accepted the rule of Aegon I Targaryen following his Conquest, despite the fact that he was in an incestuous, polygamous marriage with both his sisters, Visenya and Rhaenys. When his son Aenys was wed in 22 AC to his cousin Alyssa Velaryon, no objections were raised. However, when a marriage was proposed between Aenys's brother, Maegor, and Aenys's daughter, Rhaena, the High Septon protested, preventing the marriage from taking place.
The views regarding marriages between an uncle and a niece (or an aunt to a nephew) might differ between the Faith and the old gods. Although the High Septon protested against a possible marriage between Prince Maegor and his niece Rhaena, in the north, Serena Stark had been wed to her uncle, Edric, while her sister Sansa Stark had been wed to her uncle Jonnel Stark.
In 41 AC, when Aenys wed his daughter Rhaena and son Aegon to one another, the Faith rose in rebellion. The High Septon sent Aenys a denunciation, addressing him as "King Abomination"; pious lords and smallfolk, who had once loved Aenys, turned against him. The uprising lasted the remainder of Aenys's reign and continued throughout the reign of King Maegor I Targaryen. Peace between the Faith and the Crown was eventually reached during the reign of Jaehaerys I Targaryen.
House Targaryen has, over the years, continued their incestuous marriages. Jaehaerys I himself was wed to his younger sister Alysanne, while his children Baelon and Alyssa were married to one another. King Aegon II Targaryen was wed to his sister Helaena Targaryen, King Baelor I Targaryen had been wed to his sister Daena (although the marriage was never consummated and Baelor had the marriage annulled upon ascending the throne), King Aegon IV was wed to his sister Naerys, Prince Aelor his twin-sister Aelora, King Jaehaerys II Targaryen to his sister Shaera, and their son Aerys II Targaryen to his sister Rhaella.
King Aegon V Targaryen, once betrothed to his own sister Daella, became convinced that the incestuous marriage customs of House Targaryen were harmful. As such, Aegon and Queen Betha Blackwood betrothed four of their five children in 237 AC to sons and daughters of some of the Great Houses of the Seven Kingdoms. When his son Jaehaerys and daughter Shaera married in secret, Aegon was forced to accept the marriage. Years later, based on the prophecy made by a woods witch, Jaehaerys commanded his son Aerys and daughter Rhaella to marry one another. Whilst King Aegon V was frustrated by Jaehaerys's decision, he let his son have his way.
Incest Beyond the Wall
Incest in Essos
A Game of Thrones
Lord Stannis Baratheon, brother of King Robert I Baratheon, becomes suspicious about the paternity of Queen Cersei Lannister’s three children, Joffrey, Myrcella, and Tommen, believing they had not been fathered by her husband, King Robert I, but instead by her brother, Ser Jaime Lannister of the Kingsguard. He investigates the matter with Lord Jon Arryn, who discovers proof for Cersei’s infidelity. Before he can reveal the secret to the king, he dies.
When the king visits Winterfell with half his court, Bran Stark accidentally witnesses Queen Cersei and Ser Jaime having sex. In an attempt to keep their secret, Jaime throws Bran from the window of the tower they are in.
In King's Landing, Lord Eddard Stark discovers Queen Cersei's secret. He informs Lord Petyr Baelish of the fact, but Baelish's reaction suggests he had been aware for some time already. Eddard goes to confront Cersei, who confirms her relationship with Jaime. When King Robert I dies, Eddard attempts to prevent Joffrey from taking the throne, but is betrayed, arrested, and subsequently executed.
A Clash of Kings
Stannis Baratheon proclaims himself to be King on Dragonstone, and thereby lays claim to the Iron Throne. He has his maester, Pylos, write numerous copies of a letter in which he proclaims Cersei’s three children to be the products of her incestuous relationship with her brother, Jaime. These letters are send to the lords of the Seven Kingdoms, including the Red Keep in King’s Landing.
A Storm of Swords
A Feast for Crows
Ser Kevan Lannister makes it clear to both Cersei and Jaime that he is aware of their relationship and the paternity of Cersei's children. As part of her plot to discredit Queen Margaery Tyrell, Dowager Queen Cersei Lannister has disgraced former maester Qyburn torture the Blue Bard into confessing how he witnessed Margaery having affairs with lovers. Among those accused he names Margaery’s brother, Ser Loras Tyrell. However, Cersei knows that the lie will not be believed, on account of Loras's sexual preferences, nor be taken kindly, following his recent military success at Dragonstone, and insists the Blue Bard changes his confession.
A Dance with Dragons
When he discovers Gilly was not only Craster's daughter, but also his wife who gave birth to his son, he agrees to Jon Snow's plan to send Gilly south, stating he will not suffer "such abominations" at the Wall.
Having been taken captive by the Faith, Dowager Queen Cersei Lannister is charged with multiple crimes, including incest. She denies to the High Septon that her children were fathered by her brother instead of her husband. During her walk of atonement, the smallfolk call Cersei names, including "brotherfucker".
Bastards were common enough, but incest was a monstrous sin to both old gods and the new, and the children of such wickedness were named abominations in sept and godswood alike. The dragonkings had wed brother to sister, but they were the blood of old Valyria where such practices had been common, and like their dragons the Targaryens answered to neither gods nor men.
– Thoughts of Catelyn Stark
- Wikipedia: Incest
- A Clash of Kings, Chapter 33, Catelyn IV.
- The World of Ice & Fire, The Targaryen Kings: Aenys I.
- The World of Ice & Fire, Appendix: Lannister Lineage.
- A Feast for Crows, Chapter 16, Jaime II.
- The World of Ice & Fire, Appendix: Targaryen Lineage.
- The World of Ice & Fire, Appendix: Stark Lineage.
- The World of Ice & Fire, The Fall of the Dragons: The Year of the False Spring.
- A Clash of Kings, Appendix.
- A Storm of Swords, Chapter 68, Sansa VI.
- The World of Ice & Fire, The Reign of the Dragons: The Conquest.
- The World of Ice & Fire, The Targaryen Kings: Maegor I.
- The World of Ice & Fire, The Targaryen Kings: Jaehaerys I.
- The Sworn Sword.
- The World of Ice & Fire, The Targaryen Kings: Aegon V.
- A Dance with Dragons, Chapter 23, Daenerys IV.
- A Clash of Kings, Chapter 23, Jon III.
- A Game of Thrones, Chapter 8, Bran II.
- A Game of Thrones, Chapter 47, Eddard XIII.
- A Game of Thrones, Chapter 45, Eddard XII.
- A Game of Thrones, Chapter 49, Eddard XIV.
- A Game of Thrones, Chapter 65, Arya V.
- A Game of Thrones, Chapter 58, Eddard XV.
- A Game of Thrones, Chapter 3, Daenerys I.
- A Clash of Kings, Prologue.
- A Clash of Kings, Chapter 10, Davos I.
- A Clash of Kings, Chapter 15, Tyrion III.
- A Clash of Kings, Chapter 55, Catelyn VII.
- A Storm of Swords, Chapter 33, Samwell II.
- A Storm of Swords, Chapter 46, Samwell III.
- A Storm of Swords, Chapter 75, Samwell IV.
- A Feast for Crows, Chapter 7, Cersei II.
- A Feast for Crows, Chapter 39, Cersei IX.
- A Dance with Dragons, Chapter 3, Jon I.
- A Dance with Dragons, Chapter 54, Cersei I.
- A Dance with Dragons, Chapter 65, Cersei II.