Note/Update on 2020-06-24: I've expanded the list to include 360 games (not just Xbox One games) and to include some platformers/metroivanias.
Honourable Mentions (these games are primarily in the non-puzzle games genre but they had puzzle elements that I enjoyed:
5/5: Rise of the Tomb Raider (unlike the 2013 Tomb Raider Reboot, this game had meaty tombs (relatively at least) and great puzzles in the DLC)
5/5: Forza Horizon 4's Fortune Island DLC (this DLC had 10 simple, fun car-themed riddles as part of a treasure hunt)
5/5: Shadow of the Tomb Raider (even more puzzle-solving and tombs than Rise of the Tomb Raider)
5/5: Banjo-Kazooie: Nuts & Bolts
5/5: Batman: Arkham Asylum
5/5: Batman: Arkham City
4.5/5: Watch Dogs 1 (open world sandbox game; lots of smart-phone-related puzzles)
4/5: High on Life
Excellent, near perfect puzzle/adventure games, rated 5/5:
In Between
So Many Me
D4: Dark Dreams Don't Die
Unravel
Limbo
The Walking Dead Season 1
The Wolf Among Us
Life Is Strange
Thomas Was Alone
Brothers - A Tale of Two Sons
Inside
The Turing Test
The Witness
King's Quest
Abzu
The Sexy Brutale
Little Nightmares
What Remains Of Edith Finch
Celeste
A Way Out
Hellblade: Senua's Sacrifice
Q.U.B.E. 2
The Talos Principle
The Missing: JJ Macfield and the Island of Lost Memories
RiME
Life Is Strange 2
A Plague Tale: Innocence
Braid
Splosion Man
The Misadventures of P.B. Winterbottom
Super Meat Boy
ilomilo
Portal 2
Ms. Splosion Man
Rayman Origins
Fez
BattleBlock Theater
Rayman Legends
Guacamelee! Super Turbo Championship Edition
Ori and the Blind Forest: Definitive Edition
Return of the Obra Dinn
Manifold Garden
Ori and the Will of the Wisps
The Medium
Crash Bandicoot 4: It's About Time
Psychonauts 2
AI: The Somnium Files
Life Is Strange: True Colors
It Takes Two
Tunic
Danganronpa 2: Goodbye Despair Anniversary Edition
AI: The Somnium Files - nirvanA Initiative
Danganronpa v3: Killing Harmony Anniversary Edition
Beacon Pines
A Plague Tale: Requiem
Pentiment
The next tier of excellent puzzle/adventure games, rated 4.5/5:
The Bridge
Q.U.B.E. Director's Cut
Gone Home
The Walking Dead Season 2
Virginia
Batman by Telltale Season 1
Oxenfree
The Inner World
Tacoma
Life Is Strange Before The Storm
A Hat In Time
The Awesome Adventures of Captain Spirit
The Gardens Between
Gorogoa
SOMA
Phoenix Wright: Ace Attorney Trilogy
The Cave
Darksiders
Portal: Still Alive
Tomb Raider: Anniversary
Wandersong
The Walking Dead: The Final Season
Tell Me Why
Thimbleweed Park
Day of the Tentacle Remastered
Psychonauts
Danganronpa: Trigger Happy Havoc Anniversary Edition
Zero Escape: The Nonary Games
Zero Escape: Nine Hours, Nine Persons, Nine Doors
Zero Escape: Virtue's Last Reward
As Dusk Falls
Great puzzle/adventure games, rated 4/5:
Max: The Curse of Brotherhood
Candleman
White Night
Hue
Black The Fall
The Little Acre
A Boy and his Blob
Flockers
Lara Croft and the Temple of Osiris
Kalimba
Valiant Hearts: The Great War
Sherlock Holmes: Crimes & Punishment
Never Alone (Kisima Ingitchuna)
Pneuma: Breath of Life
Unmechanical: Extended Edition
The Fall
Stick it to the Man
Cubot - The Complexity of Simplicity
The Swapper
The Walking Dead: Michonne
Broken Sword 5: The Serpent's Curse
Teslagrad
Firewatch
Late Shift
Voodoo Vince: Remastered
Walking Dead: A New Frontier
Guardians of the Galaxy by Telltale
Unravel 2
The Walking Dead Collection
Sea of Solitude
Song of the Deep
Banjo-Kazooie
Lara Croft and the Guardian of Light
Doritos Crash Course
Outland
Beyond Good & Evil HD
Battletoads
The Touryst
Call of the Sea
Observation
Crash Bandicoot N. Sane Trilogy
Twelve Minutes
Unpacking
Last Stop
Tinykin
Immortality
3.5/5:
AER - Memories of Old
Clockwork Tales: Of Glass and Ink
Enigmatis: The Ghosts of Maple Creek
Lifeless Planet
Beyond Eyes
Her Majesty's Spiffing
Abyss: The Wraiths of Eden
TurnOn
Oceanhorn: Monster of Uncharted Seas
Back to the Future: The Game - 30th Anniversary Edition
Game of Thrones: A Telltale Games Series
Submerged
Tales from the Borderlands
Nightmares from the Deep: The Cursed Heart
Grim Legends: The Forsaken Bride
Nightmares from the Deep 2: The Siren's Call
Eventide: Slavic Fable
Enigmatis 2: The Mists of Ravenwood
Manual Samuel
Grim Legends 2: Song of the Dark Swan
Four Sided Fantasy
The Assembly
Forgotton Anne
Old Man's Journey
Stacking
The Artful Escape
3/5:
6180 The Moon
Minecraft: Story Mode - A Telltale Games Series
Contrast
The Park
Dark Arcana: The Carnival
Lost Grimoires: Stolen Kingdom
Blackwood Crossing
Eventide 2: Sorcerer's Mirror
Minecraft Story Mode Season 2
Batman by Telltale Season 2: The Enemy Within
Super Lucky's Tale
Axel & Pixel
Monkey Island 2: LeChuck's Revenge
The Secret of Monkey Island: Special Edition
Insanely Twisted Shadow Planet
Trine 2
Doritos Crash Course 2
Full Throttle Remastered
Cuphead
Telling Lies
Puzzletronics: Digital Infinite
Zero Escape: Zero Time Dilemma
2.5/5
11-11: Memories Retold
Murdered: Soul Suspect
Blues & Bullets
140
Skylar and Plux: Adventure On Clover Island
Monochroma
World to the West
Nightmares from the Deep 3: Davy Jones
Deadlight
Paradise Killer
2/5:
Fragments of Him
Whispering Willows
Gemini: Heroes Reborn
Among The Sleep
Wheels of Aurelia
Toby: The Secret Mine
Lost Grimoires 2: Shard of Mystery
The Town of Light
The Vanishing of Ethan Carter
Night In The Woods
Dreamfall Chapters
Flipping Death
The Maw
Grim Fandango Remastered
Outer Wilds
The Invisible Hours
A Memoir Blue
1.5/5
Three Fourths Home: Extended Edition
Dear Esther: Landmark Edition
The Bunker
Dreamals: Dream Quest
The Infectious Madness of Doctor Dekker
Fractured Minds
Quarrel
PHOGS!
Adios
1/5:
NERO
Albedo: Eyes from Outer Space
Narcosis
Nevermind
Honourable Mentions (these games are primarily in the non-puzzle games genre but they had puzzle elements that I enjoyed:
5/5: Rise of the Tomb Raider (unlike the 2013 Tomb Raider Reboot, this game had meaty tombs (relatively at least) and great puzzles in the DLC)
5/5: Forza Horizon 4's Fortune Island DLC (this DLC had 10 simple, fun car-themed riddles as part of a treasure hunt)
5/5: Shadow of the Tomb Raider (even more puzzle-solving and tombs than Rise of the Tomb Raider)
5/5: Banjo-Kazooie: Nuts & Bolts
5/5: Batman: Arkham Asylum
5/5: Batman: Arkham City
4.5/5: Watch Dogs 1 (open world sandbox game; lots of smart-phone-related puzzles)
4/5: High on Life
Excellent, near perfect puzzle/adventure games, rated 5/5:
In Between
So Many Me
D4: Dark Dreams Don't Die
Unravel
Limbo
The Walking Dead Season 1
The Wolf Among Us
Life Is Strange
Thomas Was Alone
Brothers - A Tale of Two Sons
Inside
The Turing Test
The Witness
King's Quest
Abzu
The Sexy Brutale
Little Nightmares
What Remains Of Edith Finch
Celeste
A Way Out
Hellblade: Senua's Sacrifice
Q.U.B.E. 2
The Talos Principle
The Missing: JJ Macfield and the Island of Lost Memories
RiME
Life Is Strange 2
A Plague Tale: Innocence
Braid
Splosion Man
The Misadventures of P.B. Winterbottom
Super Meat Boy
ilomilo
Portal 2
Ms. Splosion Man
Rayman Origins
Fez
BattleBlock Theater
Rayman Legends
Guacamelee! Super Turbo Championship Edition
Ori and the Blind Forest: Definitive Edition
Return of the Obra Dinn
Manifold Garden
Ori and the Will of the Wisps
The Medium
Crash Bandicoot 4: It's About Time
Psychonauts 2
AI: The Somnium Files
Life Is Strange: True Colors
It Takes Two
Tunic
Danganronpa 2: Goodbye Despair Anniversary Edition
AI: The Somnium Files - nirvanA Initiative
Danganronpa v3: Killing Harmony Anniversary Edition
Beacon Pines
A Plague Tale: Requiem
Pentiment
The next tier of excellent puzzle/adventure games, rated 4.5/5:
The Bridge
Q.U.B.E. Director's Cut
Gone Home
The Walking Dead Season 2
Virginia
Batman by Telltale Season 1
Oxenfree
The Inner World
Tacoma
Life Is Strange Before The Storm
A Hat In Time
The Awesome Adventures of Captain Spirit
The Gardens Between
Gorogoa
SOMA
Phoenix Wright: Ace Attorney Trilogy
The Cave
Darksiders
Portal: Still Alive
Tomb Raider: Anniversary
Wandersong
The Walking Dead: The Final Season
Tell Me Why
Thimbleweed Park
Day of the Tentacle Remastered
Psychonauts
Danganronpa: Trigger Happy Havoc Anniversary Edition
Zero Escape: The Nonary Games
Zero Escape: Nine Hours, Nine Persons, Nine Doors
Zero Escape: Virtue's Last Reward
As Dusk Falls
Great puzzle/adventure games, rated 4/5:
Max: The Curse of Brotherhood
Candleman
White Night
Hue
Black The Fall
The Little Acre
A Boy and his Blob
Flockers
Lara Croft and the Temple of Osiris
Kalimba
Valiant Hearts: The Great War
Sherlock Holmes: Crimes & Punishment
Never Alone (Kisima Ingitchuna)
Pneuma: Breath of Life
Unmechanical: Extended Edition
The Fall
Stick it to the Man
Cubot - The Complexity of Simplicity
The Swapper
The Walking Dead: Michonne
Broken Sword 5: The Serpent's Curse
Teslagrad
Firewatch
Late Shift
Voodoo Vince: Remastered
Walking Dead: A New Frontier
Guardians of the Galaxy by Telltale
Unravel 2
The Walking Dead Collection
Sea of Solitude
Song of the Deep
Banjo-Kazooie
Lara Croft and the Guardian of Light
Doritos Crash Course
Outland
Beyond Good & Evil HD
Battletoads
The Touryst
Call of the Sea
Observation
Crash Bandicoot N. Sane Trilogy
Twelve Minutes
Unpacking
Last Stop
Tinykin
Immortality
3.5/5:
AER - Memories of Old
Clockwork Tales: Of Glass and Ink
Enigmatis: The Ghosts of Maple Creek
Lifeless Planet
Beyond Eyes
Her Majesty's Spiffing
Abyss: The Wraiths of Eden
TurnOn
Oceanhorn: Monster of Uncharted Seas
Back to the Future: The Game - 30th Anniversary Edition
Game of Thrones: A Telltale Games Series
Submerged
Tales from the Borderlands
Nightmares from the Deep: The Cursed Heart
Grim Legends: The Forsaken Bride
Nightmares from the Deep 2: The Siren's Call
Eventide: Slavic Fable
Enigmatis 2: The Mists of Ravenwood
Manual Samuel
Grim Legends 2: Song of the Dark Swan
Four Sided Fantasy
The Assembly
Forgotton Anne
Old Man's Journey
Stacking
The Artful Escape
3/5:
6180 The Moon
Minecraft: Story Mode - A Telltale Games Series
Contrast
The Park
Dark Arcana: The Carnival
Lost Grimoires: Stolen Kingdom
Blackwood Crossing
Eventide 2: Sorcerer's Mirror
Minecraft Story Mode Season 2
Batman by Telltale Season 2: The Enemy Within
Super Lucky's Tale
Axel & Pixel
Monkey Island 2: LeChuck's Revenge
The Secret of Monkey Island: Special Edition
Insanely Twisted Shadow Planet
Trine 2
Doritos Crash Course 2
Full Throttle Remastered
Cuphead
Telling Lies
Puzzletronics: Digital Infinite
Zero Escape: Zero Time Dilemma
2.5/5
11-11: Memories Retold
Murdered: Soul Suspect
Blues & Bullets
140
Skylar and Plux: Adventure On Clover Island
Monochroma
World to the West
Nightmares from the Deep 3: Davy Jones
Deadlight
Paradise Killer
2/5:
Fragments of Him
Whispering Willows
Gemini: Heroes Reborn
Among The Sleep
Wheels of Aurelia
Toby: The Secret Mine
Lost Grimoires 2: Shard of Mystery
The Town of Light
The Vanishing of Ethan Carter
Night In The Woods
Dreamfall Chapters
Flipping Death
The Maw
Grim Fandango Remastered
Outer Wilds
The Invisible Hours
A Memoir Blue
1.5/5
Three Fourths Home: Extended Edition
Dear Esther: Landmark Edition
The Bunker
Dreamals: Dream Quest
The Infectious Madness of Doctor Dekker
Fractured Minds
Quarrel
PHOGS!
Adios
1/5:
NERO
Albedo: Eyes from Outer Space
Narcosis
Nevermind
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