The original PlayStation, now referred to as the PS1, was home to tons of great games, despite the PS2 being the much more popular console. Like many retro consoles, the PS1 is home to some incredibly rare games and some incredibly expensive retro games, but it was also home to many games that were never released outside of Japan. For one reason or another, some games were never translated, and because of that, were never given a North American release, despite being excellent games. While the reason why an individual game was never released outside of Japan, some of these games can be played with fan translations via PS1 emulation.

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4 Policenauts
Hideo Kojima's point-and-click adventure

Source: Konami
Prior to directing Metal Gear Solid, Hideo Kojima and Konami made Policenauts, a point-and-click anime-inspired adventure game about a detective in the future. The original PlayStation was the third platform to be released after the NEC PC-9821 and 3DO, but the PlayStation was its biggest platform. Never officially translated or released outside of Japan, Policenauts follows Jonathan Ingram, one of the five "Policenauts," officers trained as astronauts to police the new space colony. He got lost adrift in space, with his suit putting him in cryo sleep, resulting in him being discovered 25 years later. He returned to Los Angeles as a detective, but when his former wife is killed and her new husband goes missing, he must return to the colony to solve the mystery. It's a point-and-click game, where you pick parts of the environment to examine and choose dialogue options when speaking with people. Policenauts was received well at the time of release, and interest grew after Kojima became a household name in gaming, but it still hasn't received an official English translation.

Policenauts
Released July 29, 1994
ESRB e
Developer(s) Konami
3 Kowai Shashin
A haunted video game

Source: Media Entertainment
Kowai Shashin was not particularly popular at its initial release, but its focus on photography capitalized on the popularity of scary photos with "real" ghosts in them (via Grimoire of Horror). The game doesn't feature a narrative through line and instead presents players with a series of real-life photographs, which contain spirits that need to be excised. You had to follow the steps of Kuji-Kiri, which is a combination of hand gestures and syllables meant to invoke spiritual powers, used by some to excise spirits, as shown in the recent film Exhuma. Kowai Shashin was well known in Japan thanks to the studio's marketing strategy, which involved them promoting the in-game images as genuine haunted images taken by a paranormal photographer, with the cursed artifacts causing havoc during development. While made up of promotional material, the strategy was moderately successful in convincing some people that the game is genuinely haunted. However, the unique gameplay and focus on real-world photographs make this a unique game that should have been released globally.
2 Mizzurna Falls
Twin Peaks, the video game

Source: Human Entertainment
Mizzurna Falls is an open-world mystery game, where you play as American high schooler Matthew Williams. Set in a fictional town in Colorado, the game has you attempt to solve the death of your classmate, who was seemingly attacked by a bear, before a second crime makes the case far more suspicious. Mizzurna Falls takes place over seven days, where time is constantly moving, and you have to explore the town with your car and find clues to solve the crimes. The snowy mountain town and some of the more surreal aspects of the narrative feel directly inspired by David Lynch's Twin Peaks, but its late 90s American town is deeply interesting, due to it being developed by a Japanese team. It's a predecessor to modern open-world games, and the mix of horror with a fairly realistic narrative made it a unique horror game at the time of its release, and one that could have succeeded with Western audiences.
1 Pepsiman
A strange corporate tie-in

One of the odder Japan-only PlayStation 1 releases, Pepsiman is an early infinite runner game, like modern mobile games Temple Run and Subway Surfers, where you control an endlessly running Pepsiman while you attempt to collect Pepsi cans and avoid obstacles. This oddity gave it cult-classic status, partially thanks to the use of the unsuccessful Japan-only mascot, Pepsiman. It was released as a budget title, prompting reviewers to cut it some slack, but considering its existence as marketing material, it falls into the shockingly competent brand games, like the Burger King games and Doritos Crash Course. It was never released outside of Japan, partially due to Pepsiman himself being a regional mascot, but also due to relatively poor sales. It might seem odd to ask for a corporate tie-in game that was only released in Japan when there were more artistic games to choose from, but this release is such a strange relic of the 90s and how marketing looked during that time, that it's almost an important piece of history.
Excellent games limited to fan translations
While many Japan-only games from that time period have received fan translations, including most of the games listed above that can be enjoyed via emulation, there are plenty of important and great video games that are inaccessible due to not being released outside of Japan. While issues with licenses and now defunct game studios make it almost impossible for these games to get official translations, there are important parts of the history of video games that aren't regarded the way they should be, due to these barriers to people who want to play them.