Arya
23 episodes of Game of Thrones carry this thread, 23h in all — 18 of them are in The Essentials.
Arc membership is derived from each episode's own title and summary text. It shows where a thread is foregrounded, not every episode it touches.
In airing order

Tyrion joins his father's army with unexpected allies. Events in King's Landing take a turn for the worse as Arya's lessons are put to the test.

Stannis uses Ser Davos to seek out new allies for his war with the Lannisters. On the road north, Arya confides in Gendry. Robb Stark sends Theon Greyjoy to win an alliance with his father and the fierce warriors of the Iron Islands. Cersei and Tyrion clash on how to rule in King's Landing.

Tyrion attempts to restrain Joffrey's cruelty. Catelyn attempts to broker a peace between Stannis and Renly. Daenerys and her followers arrive at the great city of Qarth and hope to find refuge there. Arya and Gendry arrive at Harrenhal, a great castle now under Lannister occupation.

Confusion rages in the Stormlands in the wake of a devastating reversal. Catelyn must flee with a new ally, whilst Littlefinger sees an opportunity in the chaos. Theon seeks to prove himself to his father in battle. Arya receives a promise from the enigmatic Jaqen H'ghar. The Night's Watch arrives at the Fist of the First Men. Daenerys Targaryen receives a marriage proposal.

Arya has a surprise visitor; Dany vows to take what is hers; Joffrey meets his subjects; Qhorin gives Jon a chance to prove himself.

Theon holds the fort; Arya calls in her debt with Jaqen; Robb is betrayed; Stannis and Davos approach their destination.

Tyrion awakens to a changed situation. King Joffrey doles out rewards to his subjects. As Theon stirs his men to action, Luwin offers some final advice. Brienne silences Jaime; Arya receives a gift from Jaqen; Dany goes to a strange place; Jon proves himself to Qhorin.

Sansa says too much. Shae asks Tyrion for a favor. Jaime finds a way to pass the time. Arya runs into the Brotherhood Without Banners.

The Night's Watch takes stock. Varys meets his better. Arya is taken to the commander of the Brotherhood. Daenerys exchanges a chain for a Whip.

Tyrion welcomes a guest to King's Landing. At Castle Black, Jon Snow finds himself unwelcome. Dany is pointed to Meereen, the mother of all slave cities. Arya runs into an old friend.

Tyrion ponders his options. Tywin extends an olive branch. Sam realizes Castle Black isn't safe, and Jon proposes a bold plan. The Hound teaches Arya the way things are. Dany chooses her Champion.

Arya arrives in Braavos; Brienne and Podrick find danger while traveling; Cersei worries about Myrcella in Dorne when Ellaria Sand seeks revenge for Oberyn's death; Jon is tempted by Stannis.

Cersei meets the High Sparrow after learning of a clergyman's embarrassing tale. Meanwhile, Davos talks to Jon about the future of Winterfell, where Ramsay Snow has just learned the identity of his future bride; Arya grows impatient doing menial tasks in the House of Black and White; and Tyrion searches for more comfortable surroundings on a long trip with Varys.

Arya trains. Jorah and Tyrion run into slavers. Trystane and Myrcella make plans. Jaime and Bronn reach their destination. The Sand Snakes attack.

Arya makes progress in her training. Sansa confronts an old friend. Cersei struggles. Jon travels.

Stannis confronts a troubling decision. Jon returns to The Wall. Mace visits the Iron Bank. Arya encounters someone from her past. Dany reluctantly oversees a traditional celebration of athleticism.

Cersei seeks forgiveness; Jon faces a new challenge; Arya plots to cross a name off her list; Tyrion sees a familiar face; and Daenerys finds herself surrounded by strangers.

Daenerys meets her future. Bran meets the past. Tommen confronts the High Sparrow. Arya trains to be No One. Varys finds an answer. Ramsay gets a gift.

Tyrion seeks a strange ally. Bran learns a great deal. Brienne goes on a mission. Arya is given a chance to prove herself.

An old foe comes back into the picture. Gilly meets Sam's family. Arya faces a difficult choice. Jaime faces off against the High Sparrow.

The High Sparrow eyes another target. Jaime confronts a hero. Arya makes a plan. The North is reminded.

Jaime encounters a hero; the High Sparrow fixates on another prey; Arya hatches a new plan; Yara and Theon plot their next move; Olenna and Cersei discuss their families' futures. While Jaime weighs his options, Cersei answers a request. Tyrion's plans bear fruit. Arya faces a new test.

Arya gets to the final destination. Daenerys takes it upon herself to strike back.