Game compatibility list?

Solution 1:

Below is a list of supported games that I sourced from Wikipedia (Node.js gist).

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• AKB1/149 Ren'ai Sōsenkyo
• Akiba's Trip 2
• Amagami Ebicore+
• Amnesia V Edition
• Ano Ko wa Ore kara Hanarenai
• Assault Gunners
• Atelier Ayesha Plus: The Alchemist of Dusk
• Atelier Meruru Plus: The Apprentice of Arland
• New Atelier Rorona
• Atelier Totori Plus: The Adventurer of Arland
• Bitter Smile
• BlazBlue: Chronophantasma
• BlazBlue: Continuum Shift Extend
• Chō no Doku Hana no Kusari: Taishō Enren Ibun
• Clannad
• Conception II: Children of the Seven Stars
• Criminal Girls Invitation
• Cure Mate Club
• Dairansō Dash or Dasshu!!
• Damascus Gear Tokyo Hajime-sen
• Danball Senki W
• Danganronpa 1 & 2 Reloaded
• Danganronpa: Trigger Happy Havoc [Asia (Hong Kong, Taiwan, SE Asia) region only]
• Dead or Alive 5+
• Deception IV: Blood Ties
• Dekamori Senran Kagura
• Demon Gaze
• Diabolik Lovers Limited V Edition
• Disgaea 3: Absence of Detention [Japan region only]
• Disgaea 4: A Promise Revisited
• Dragon Ball Z: Battle of Z
• Dragon's Crown
• Dragon's Dogma Quest
• Dungeon Hunter: Alliance
• Dynasty Warriors 8 Xtreme Legends
• Earth Defense Force 2017 Portable
• escapeVektor
• Exstetra
• Fate/stay night [Réalta Nua]
• Final Fantasy X HD
• Final Fantasy X-2 HD
• Freedom Wars
• Furuiro Meikyuu Rondo: La Roue de fortune
• F1 2011
• Getsuei Gakuen: Kou
• Ginsei Shougi
• God Eater 2
• God of War Collection
• Golden Time: Vivid Memories
• Grisaia no Kajitsu: Le Fruit De La Grisaia
• Guilty Gear XX Accent Core Plus R
• Gundam Breaker
• Haiyore! Nyaruko-san: Meijo shigatai Game no you na mono
• Hatsune Miku: Project DIVA f
• Hatsune Miku: Project DIVA F 2nd
• Hakuōki: Kyōkaroku
• Hakuōki SSL
• Hotaru no Nikki
• Hotchkiss
• Hyperdimension Neptunia: Producing Perfection
• Hyperdimension Neptunia Re;Birth
• Hyperdimension Neptunia Re;Birth 2: Sisters Generation
• Ima Sugu Oniichan ni Imōto da tte Iitai!
• Infinite Stratos 2: Ignition Hearts
• J-Stars Victory Vs
• Jikkyō Powerful Pro Yakyū 2013
• Kajiri Kamui Kagura: Akebono no Hikari
• Kidō Senshi Gundam SEED Battle Destiny
• Killzone: Mercenary [With Q1 2014 patch[105]]
• Kud Wafter Converted Edition
• Labyrinth Cross Blood: Infinity
• Liberation Maiden SIN
• Limbo
• Little Busters! Converted Edition
• Lord of Apocalypse
• Lovely Quest Unlimited
• Lumines Electronic Symphony
• Mahjong Fight Club: Shinsei Zenkoku Taisen Han
• Magical Beat
• Malicious Rebirth
• Mato Kurenai Yuugekitai: Tokyo Twilight Ghosthunters
• Memories Off 6 Complete
• Memories Off: Yubikiri no Kioku
• Michael Jackson: The Experience [Asia region only]
• Million Arthur
• Mind Zero
• Moe Moe Daisensou Gendaibaan++
• MotorStorm: RC
• Moujuutsukai to Ouji-sama
• Muramasa Rebirth
• Naitei! Shūkatsu Kanzen Taisaku ES, SPI, Mensetsu
• Nekurebo Gyōsei Shoshi Shiken
• Nekurebo Ōyōjōhō Gijutsusha Shiken
• Nekurebo Kihonjōhō Gijutsusha Shiken
• Nekurebo Kaigo Fukushi-shi Shiken
• Nekurebo Care Manager Shiken
• Nekurebo Eiken
• Nekurebo Eibunhō Tettei Tokkun
• Nekurebo Jōhō Security Specialist Shiken, Network Specialist Shiken
• Nekurebo IT Passport Shiken
• Nekurebo Sharō-shi Shiken
• Nekurebo Takken-shi Shiken
• Nekurebo FP Ginō Kentei Shiken Ni-kyū
• Nekurebo FP Ginō Kentei Shiken San-kyū
• Nekurebo Hisho Kentei Shiken
• Nekurebo Chūshōkigō Shindan-shi Shiken 1
• Nekurebo Chūshōkigō Shindan-shi Shiken 2
• Nekurebo Shakai Fukushi-shi Shiken
• Natural Doctrine
• Nikoli no Puzzle V: Bijutsukan
• Nikoli no Puzzle V: Hashiwokakero
• Nikoli no Puzzle V: Heyawake
• Nikoli no Puzzle V: Hitori ni Shite Kure
• Nikoli no Puzzle V: Kakuro
• Nikoli no Puzzle V: Masyu
• Nikoli no Puzzle V: Numberlink
• Nikoli no Puzzle V: Nurikabe
• Nikoli no Puzzle V: Shikaku
• Nikoli no Puzzle V: Shugyoku no Jū-ni Puzzle
• Nikoli no Puzzle V: Yajilin
• Nikoli's Slitherlink V
• Nikoli's Sudoku V
• Nihon Mahjong Renmei Kōnin Motto Nijū-bai! Mahjong ga Tsuyoku Naru Hōhō: Hatsu Chūkyū-sha-hen
• Nihon Pro Mahjong Renmei Suisen Tokoton Mahjong! Joryū Pro ni Chōsen! Tetsuman Megami Special
• Ninja Gaiden Sigma Plus
• Ninja Gaiden Sigma Plus 2
• Nobunaga's Ambition: Tendou
• One Piece: Pirate Warriors 2
• Ore ni Hatarakette Iwaretemo Otsu HD
• Ore no Shikabane wo Koete Yuke 2
• Oretachi ni Tsubasa wa Nai
• Persona 4: Golden
• Phantom Breaker: Battle Grounds
• Pixeljunk Monsters Ultimate HD
• Power Pro Stadium
• Present for You
• Princess Arthur
• Princess Strike!
• Pro Yakyū Spirits 2013
• Pro Yakyū Spirits 2014
• Puella Magi Madoka Magica: The Battle Pentagram
• Puyo Puyo Tetris
• Ragnarok Odyssey
• Ragnarok Odyssey Ace
• Ratchet & Clank QForce
• Rayman Legends
• Rayman Origins
• Rewrite
• Robotics;Notes Elite
• Ro-Kyu-Bu! Naisho no Shutter Chance
• Romance of the Three Kingdoms XII
• Rozen Maiden
• Rui wa tomo wo yobu
• Sakurasou no Pet na Kanojo
• Samurai Warriors 2 with Xtreme Legends & Empires HD Version.
• Samurai Warriors 4
• Sangokuhime 2
• Sangokuhime 3
• Sangokuhime 4
• Sangoku Koi Senki
• Senran Kagura Shinovi Versus: Shojo-tachi no Shomei
• Shantae: Half-Genie Hero
• Shin Gundam Musou
• Slotter Mania V: Highschool of the Dead
• Slotter Mania V: Zettai Shoukeki II
• Sorcery Saga: Curse of the Great Curry God
• Soul Sacrifice
• Soul Sacrifice Delta
• Spelunker Collection
• Spelunky
• Steins;Gate
• Steins;Gate: Hiyoku Renri no Darling
• Steins;Gate: Senkei Kōsoku no Phenogram
• Sūgaku-ryoku-ō Jōkyū
• Sūgaku-ryoku-ō Shokyū
• Sūgaku-ryoku-ō Chūkyū
• Super Robot Wars Taisen OG Saga Masou Kishin 3: Pride of Justice
• 3rd Super Robot Wars Z Jigoku-hen
• Sword Art Online: Hollow Fragment
• Tales of Innocence R
• Tenshi Tsuki no Shoujo
• The Legend of Heroes: Sen no Kiseki
• The Legend of Heroes: Zero no Kiseki Evolution
• The Legend of Heroes: Ao no Kiseki Evolution
• Time Travelers
• TOEIC Test Jissen Tokkun
• TOEIC Test Jissen Tokkun 2
• Tokushu Houdoubu
• Tokyo New World Record: Operation Abyss
• Toro's Friend Network
• Tottemo E Mahjong
• Touch My Katamari [Asia (Hong Kong, Taiwan, SE Asia) region only]
• Toukiden
• Ultimate Marvel vs. Capcom 3
• Valhalla Knights 3
• Valhalla Knights 3 Gold
• Warriors Orochi 3 Ultimate
• When this song is over
• When Vikings Attack
• White Album 2: Shiawase no Mukougawa
• Winning Post 7 2013
• Winning Post 8
• Xblaze Code: Embryo
• Yahari Game Demo Ore no Seishun Love-Kome wa Machigatteiru
• Ys: Memories of Celceta

Solution 2:

One main problem is that many SONY provided lists will be region-specific. It's extremely difficult to be certain that any list is fully complete or current.

I would assume the most complete list would be available on the Japanese Playstation site, but you'd probably want to run that through some google translate or the like. I'm unclear on the compatibility of titles between regions (ie. taking a game from one region and using it in a vita tv from a different region) so I'm not sure if this helps you (as you've not specified a region), but whether that works could be a separate question anyways. If games are supported across regions, that makes a complete list even harder to pin down as it would require trying all games from all regions in order to be complete.