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• The Hound
  Why: For killing Mycah, the butcher's boy.
  Status: Dead. Cleganebowl.

 
• Meryn Trant
  Why: For (presumably) killing Syrio Forel.
  Status: Dead. Arya slit his throat in a Braavosi brothel where Meryn was abusing underage girls.

 
• Cersei Lannister
  Why: For her role in Ned Stark's death.
  Status: Dead.

 
• Joffrey
  Why: For ordering Ned Stark's execution.
  Status: Dead. Joffrey was poisoned by Olenna Tyrell and Petyr Baelish at his wedding to Margaery. Unfortunately, Arya's sister Sansa was suspected of the murder and had to go on the run.

 
• Ilyn Payne
  Why: For executing Ned Stark.
  Status: Alive - as far as we know.

 
• Polliver
  Why: For killing Lommy, stealing Needle and the torture at Harrenhal.
  Status: Dead. Arya killed him after a chance encounter at an inn.

 
• The Mountain
  Why: For the torture at Harrenhal
  Status: Dead. Cleganebowl.

 
• Rorge
  Why: For the torture at Harrenhal and threatening to rape her.
  Status: Dead. Arya killed him after Rorge and Biter attacked her and the Hound.

 
• Walder Frey
  Why: For orchestrating the Red Wedding
  Status: Dead. As of the Season 6 finale Arya used her assassin skills (including face-changing!) to infiltrate Riverrun and kill him

 
• Tywin Lannister
  Why: For orchestrating the Red Wedding.
  Status: Dead. Tyrion killed his father with a crossbow while Tywin was using the toilet.

 
• Melisandre
  Why: For kidnapping Gendry.
  Status: Dead.

 
• Beric Dondarrion
  Why: For selling Gendry to Melisandre.
  Status: Dead.

 
• Thoros of Myr
  Why: For selling Gendry to Melisandre.
  Status: Dead. Mauled by undead polar bear. Succumbs to wounds and cold.

• The Hound
  Why: For killing Mycah, the butcher's boy.
  Status: Dead. Cleganebowl.

• Meryn Trant
  Why: For (presumably) killing Syrio Forel.
  Status: Dead. Arya slit his throat in a Braavosi brothel where Meryn was abusing underage girls.

• Cersei Lannister
  Why: For her role in Ned Stark's death.
  Status: Dead.

• Joffrey
  Why: For ordering Ned Stark's execution.
  Status: Dead. Joffrey was poisoned by Olenna Tyrell and Petyr Baelish at his wedding to Margaery. Unfortunately, Arya's sister Sansa was suspected of the murder and had to go on the run.

• Ilyn Payne
  Why: For executing Ned Stark.
  Status: Alive - as far as we know.

• Polliver
  Why: For killing Lommy, stealing Needle and the torture at Harrenhal.
  Status: Dead. Arya killed him after a chance encounter at an inn.

• The Mountain
  Why: For the torture at Harrenhal
  Status: Dead. Cleganebowl.

• Rorge
  Why: For the torture at Harrenhal and threatening to rape her.
  Status: Dead. Arya killed him after Rorge and Biter attacked her and the Hound.

• Walder Frey
  Why: For orchestrating the Red Wedding
  Status: Dead. As of the Season 6 finale Arya used her assassin skills (including face-changing!) to infiltrate Riverrun and kill him

• Tywin Lannister
  Why: For orchestrating the Red Wedding.
  Status: Dead. Tyrion killed his father with a crossbow while Tywin was using the toilet.

• Melisandre
  Why: For kidnapping Gendry.
  Status: Dead.

• Beric Dondarrion
  Why: For selling Gendry to Melisandre.
  Status: Dead.

• Thoros of Myr
  Why: For selling Gendry to Melisandre.
  Status: Dead. Mauled by undead polar bear. Succumbs to wounds and cold.

Because he sold Gendry out to Melisandre.

Note that he's not on her kill list in the books, only in the TV show.

The full list from the show is as follows (more or less copied from here; spoilers including from S7):

• The Hound
  Why: For killing Mycah, the butcher's boy.
  Status: Alive. Although Arya likely believes otherwise after she left him for dead following his battle with Brienne of Tarth.

• Meryn Trant
  Why: For (presumably) killing Syrio Forel.
  Status: Dead. Arya slit his throat in a Braavosi brothel where Meryn was abusing underage girls.

• Cersei Lannister
  Why: For her role in Ned Stark's death.
  Status: Alive - for now.

• Joffrey
  Why: For ordering Ned Stark's execution.
  Status: Dead. Joffrey was poisoned by Olenna Tyrell and Petyr Baelish at his wedding to Margaery. Unfortunately, Arya's sister Sansa was suspected of the murder and had to go on the run.

• Ilyn Payne
  Why: For executing Ned Stark.
  Status: Alive.

• Polliver
  Why: For killing Lommy, stealing Needle and the torture at Harrenhal.
  Status: Dead. Arya killed him after a chance encounter at an inn.

• The Mountain
  Why: For the torture at Harrenhal
  Status: Alive-ish. Qyburn resurrected the Mountain as Ser Robert Strong after the warrior was fatally poisoned by Oberyn Martell.

• Rorge
  Why: For the torture at Harrenhal and threatening to rape her.
  Status: Dead. Arya killed him after Rorge and Biter attacked her and the Hound.

• Walder Frey
  Why: For orchestrating the Red Wedding
  Status: Dead. As of the Season 6 finale Arya used her assassin skills (including face-changing!) to infiltrate Riverrun and kill him

• Tywin Lannister
  Why: For orchestrating the Red Wedding.
  Status: Dead. Tyrion killed his father with a crossbow while Tywin was using the toilet.

• Melisandre
  Why: For kidnapping Gendry.
  Status: Alive and old af.

• Beric Dondarrion
  Why: For selling Gendry to Melisandre.
  Status: Alive. (Although Beric has died and been resurrected at least six times.)

• Thoros of Myr
  Why: For selling Gendry to Melisandre.
  Status: Dead. Mauled by undead polar bear. Succumbs to wounds and cold.

Because he sold Gendry out to Melisandre.

Note that he's not on her kill list in the books, only in the TV show.

The full list from the show is as follows (list more or less copied from here, updated with status including spoilers from S8):

• The Hound
  Why: For killing Mycah, the butcher's boy.
  Status: Dead. Cleganebowl.

• Meryn Trant
  Why: For (presumably) killing Syrio Forel.
  Status: Dead. Arya slit his throat in a Braavosi brothel where Meryn was abusing underage girls.

• Cersei Lannister
  Why: For her role in Ned Stark's death.
  Status: Dead.

• Joffrey
  Why: For ordering Ned Stark's execution.
  Status: Dead. Joffrey was poisoned by Olenna Tyrell and Petyr Baelish at his wedding to Margaery. Unfortunately, Arya's sister Sansa was suspected of the murder and had to go on the run.

• Ilyn Payne
  Why: For executing Ned Stark.
  Status: Alive - as far as we know.

• Polliver
  Why: For killing Lommy, stealing Needle and the torture at Harrenhal.
  Status: Dead. Arya killed him after a chance encounter at an inn.

• The Mountain
  Why: For the torture at Harrenhal
  Status: Dead. Cleganebowl.

• Rorge
  Why: For the torture at Harrenhal and threatening to rape her.
  Status: Dead. Arya killed him after Rorge and Biter attacked her and the Hound.

• Walder Frey
  Why: For orchestrating the Red Wedding
  Status: Dead. As of the Season 6 finale Arya used her assassin skills (including face-changing!) to infiltrate Riverrun and kill him

• Tywin Lannister
  Why: For orchestrating the Red Wedding.
  Status: Dead. Tyrion killed his father with a crossbow while Tywin was using the toilet.

• Melisandre
  Why: For kidnapping Gendry.
  Status: Dead.

• Beric Dondarrion
  Why: For selling Gendry to Melisandre.
  Status: Dead.

• Thoros of Myr
  Why: For selling Gendry to Melisandre.
  Status: Dead. Mauled by undead polar bear. Succumbs to wounds and cold.

Because he sold Gendry out to Melisandre.

Note that he's not on her kill list in the books, only in the TV show.

The full list from the show is as follows (more or less copied from here; possible spoilers):

• The Hound
  Why: For killing Mycah, the butcher's boy.
  Status: Alive. Although Arya likely believes otherwise after she left him for dead following his battle with Brienne of Tarth.

• Meryn Trant
  Why: For (presumably) killing Syrio Forel.
  Status: Dead. Arya slit his throat in a Braavosi brothel where Meryn was abusing underage girls.

• Cersei Lannister
  Why: For her role in Ned Stark's death.
  Status: Alive - for now.

• Joffrey
  Why: For ordering Ned Stark's execution.
  Status: Dead. Joffrey was poisoned by Olenna Tyrell and Petyr Baelish at his wedding to Margaery. Unfortunately, Arya's sister Sansa was suspected of the murder and had to go on the run.

• Ilyn Payne
  Why: For executing Ned Stark.
  Status: Alive.

• Polliver
  Why: For killing Lommy, stealing Needle and the torture at Harrenhal.
  Status: Dead. Arya killed him after a chance encounter at an inn.

• The Mountain
  Why: For the torture at Harrenhal
  Status: Alive-ish. Qyburn resurrected the Mountain as Ser Robert Strong after the warrior was fatally poisoned by Oberyn Martell.

• Rorge
  Why: For the torture at Harrenhal and threatening to rape her.
  Status: Dead. Arya killed him after Rorge and Biter attacked her and the Hound.

• Walder Frey
  Why: For orchestrating the Red Wedding
  Status: Dead. As of the Season 6 finale Arya used her assassin skills (including face-changing!) to infiltrate Riverrun and kill him

• Tywin Lannister
  Why: For orchestrating the Red Wedding.
  Status: Dead. Tyrion killed his father with a crossbow while Tywin was using the toilet.

• Melisandre
  Why: For kidnapping Gendry.
  Status: Alive and old af.

• Beric Dondarrion
  Why: For selling Gendry to Melisandre.
  Status: Alive. (Although Beric has died and been resurrected at least six times.)

• Thoros of Myr
  Why: For selling Gendry to Melisandre.
  Status: Dead. Mauled by undead polar bear. Succumbs to wounds and cold.

Because he sold Gendry out to Melisandre.

Note that he's not on her kill list in the books, only in the TV show.

The full list from the show is as follows (more or less copied from here; spoilers including from S7):

• The Hound
  Why: For killing Mycah, the butcher's boy.
  Status: Alive. Although Arya likely believes otherwise after she left him for dead following his battle with Brienne of Tarth.

• Meryn Trant
  Why: For (presumably) killing Syrio Forel.
  Status: Dead. Arya slit his throat in a Braavosi brothel where Meryn was abusing underage girls.

• Cersei Lannister
  Why: For her role in Ned Stark's death.
  Status: Alive - for now.

• Joffrey
  Why: For ordering Ned Stark's execution.
  Status: Dead. Joffrey was poisoned by Olenna Tyrell and Petyr Baelish at his wedding to Margaery. Unfortunately, Arya's sister Sansa was suspected of the murder and had to go on the run.

• Ilyn Payne
  Why: For executing Ned Stark.
  Status: Alive.

• Polliver
  Why: For killing Lommy, stealing Needle and the torture at Harrenhal.
  Status: Dead. Arya killed him after a chance encounter at an inn.

• The Mountain
  Why: For the torture at Harrenhal
  Status: Alive-ish. Qyburn resurrected the Mountain as Ser Robert Strong after the warrior was fatally poisoned by Oberyn Martell.

• Rorge
  Why: For the torture at Harrenhal and threatening to rape her.
  Status: Dead. Arya killed him after Rorge and Biter attacked her and the Hound.

• Walder Frey
  Why: For orchestrating the Red Wedding
  Status: Dead. As of the Season 6 finale Arya used her assassin skills (including face-changing!) to infiltrate Riverrun and kill him

• Tywin Lannister
  Why: For orchestrating the Red Wedding.
  Status: Dead. Tyrion killed his father with a crossbow while Tywin was using the toilet.

• Melisandre
  Why: For kidnapping Gendry.
  Status: Alive and old af.

• Beric Dondarrion
  Why: For selling Gendry to Melisandre.
  Status: Alive. (Although Beric has died and been resurrected at least six times.)

• Thoros of Myr
  Why: For selling Gendry to Melisandre.
  Status: Dead. Mauled by undead polar bear. Succumbs to wounds and cold.