Browsing the archives, we've had lots of discussions about Japanese Mega CD games, but it doesn't look like we have a single thread that:
(a) lists all the Japanese exclusives,
(b) describes them a bit,
(c) talks about whether they're playable if you don't speak Japanese,
(d) talks about whether they're exclusive to the Mega CD and/or available elsewhere in English, and
(e) talks about compatibility on US/EU hardware with a hacked BIOS (i.e. whether they have hardcoded region lockout).
So I thought I'd start one. Work in progress! I'll edit the first post as new info comes in, either from your posts or my research. The archived SegaBase site was a big help with the more obscure games.
Titles in blue are linked to the corresponding Sega-16 review.
A Rank Thunder Tanjouhen
RPG. Unplayable without knowing Japanese.
After Armageddon Gaiden
RPG. Unplayable without knowing Japanese. Featured in the Sega-16 article Left in Japan.
RPG. Unplayable without knowing Japanese. Dungeon crawler. Here's a gameplay video.
RPG. Unplayable without knowing Japanese. Featured in Left in Japan. At least one Sega-16 member doesn't think much of it. A walkthrough is available at Gamefaqs. Here's a review at Mobygames and a gameplay video.
Side-scrolling beat-'em-up. Mega CD exclusive. Cutscenes, title screen and closing credits are in Japanese, but completely playable without knowing the language. Works for me (WFM) on US hardware with Everdrive.
RPG. Allegedly playable without knowing Japanese, if you use Zigfried's guide cited in Melf's review. Allegedly a very lengthy dungeon crawler. Featured in Left in Japan, and reviewed by Melf in March 2012.
Arslan Senki [The Heroic Legend of Arslan]
RPG. Unplayable without knowing Japanese. Racketboy calls it a "turn-based strategy RPG". Featured in Left in Japan. Review at Defunct Games.
Bakuden: The Unbalanced Zone
A "musical action-adventure game", or that's what this guy says at least. Also on the Turbo CD.
RPG. Unplayable without knowing Japanese. Also on the MSX and SNES.
Capcom no Quiz: Tonosama no Yabou
According to this site, a historical quiz game. I'd imagine you actually have to be Japanese to play this one.
Soccer sim. Probably playable for non-Japanese speakers?
Cosmic Fantasy Stories
RPG. Apparently somewhat playable without the language. Two games in one, both ported from the PC Engine. Featured in Left in Japan. Cosmic Fantasy 2 was released in English for the Turbo Duo. Review at Mobygames.
Platformer. Cutscenes are in Japanese (and allegedly numerous). Playable without the language.
RPG. Unplayable without knowing Japanese. Apparently hard to find. Featured in Left in Japan.
Death Bringer: The Knight of Darkness
RPG. Unplayable without knowing Japanese. Dungeon crawler.
Graphic adventure. Unplayable without knowing Japanese.
Shooter/platformer. Playable without Japanese.
Dynamic Country Golf
Golf game (shockingly enough). Port from Sega System 24 arcade game. Should be playable without the language, I'd think?
Platformer. Pretty much identical to the cart version, except with added cutscenes (in Japanese) and Redbook audio. 100% playable w/o Japanese language. WFM on US hardware w/ Everdrive.
Eegawa Suguro no Super League [Super League CD Deluxe]
Baseball game. Sequel to Super League CD (listed below).
F-1 Circus CD
Racing game. Apparently quite different from the cart version.
Faeria (aka Fhey Area)
RPG. In Japanese, but Racketboy and Left in Japan say it's somewhat playable without language skills. Zigfried has written a walkthrough of the game.
Funky Horror Band
RPG. Unplayable without knowing Japanese. Heavily text-based. A fan-translation may be in the pipeline.
Gambler Jikko Chuushinha 2
Mahjongg game. Apparently it's quite a good one if you're into that sort of thing.
Game no Kanzume Vol. 1 & 2 [Sega Games Can Vol. 1 & 2]
Game collections, most of which are available elsewhere and/or are easily playable without Japanese. The exceptions are the Phantasy Star text adventures, which have recently been translated.
Genei Toshi: Illusion City
RPG. Completely unplayable without knowing Japanese. A translation has been attempted; current status unknown. Featured in Left in Japan. Poster McMasters notes that "A translation of the MSX Turbo R version was released a few years ago but the last 25% of the game was untranslated." Here's a review at Mobygames.
Genghis Khan II: Clan of the Gray Wolf [Aoki Ookami to Shiroki Mejika: Genchou Hishi]
Simulation/strategy. Probably not playable without Japanese, but ported to a zillion other systems. That includes an English version on the Genesis/MD, to which this adds Redbook audio and not much else, apparently.
Fighter. Supposedly just the cart version with Redbook audio, more or less, so language shouldn't be an issue.
Ishii Hisaichi no Daisekai [Hisaichi Ishii's Political World]
A political sim? With a title like this, I don't think there's much hope for non-Japanese players.
Jango World Cup
Mahjongg game (not soccer/football as I'd guessed). Supports four players, or so I'm told.
Mahou no Shoujo: Silky Lip
RPG. Unplayable without knowing Japanese. Heavily text-based.
Space RPG, a la Starflight. Probably unplayable without knowing Japanese. Port from MSX and/or PC Engine. Featured in Left in Japan.
Might and Magic III: Isles of Terra
RPG. Probably unplayable without knowing Japanese. PC version, in English, is widely available. Featured in Left in Japan.
Rail shooter. Arcade port, later ported to PSX and Saturn. The whole game is in English.
Ninja Warriors, The
Beat-'em-up. Arcade port. 100% playable in English -- in fact, the whole game is in English, including audio! Only the subtitles for the story scenes are in Japanese.
Nobunaga no Yabou: Haouden
Strategy/sim. Another entry in the long-running series from Koei. Also on the Mega Drive, SNES, and 3DO, but I don't think any of those were translated. If you don't speak the language, it's probably better to stick with one of the localized games in the series.
RPG/graphic adventure set aboard an ocean liner in 1907. Probably not playable without Japanese. Ported (?) from PC-98.
Pro Yakyuu Super League CD
Baseball game. Apparently it's almost the same as the cart version, just with added Redbook audio (and maybe FMVs). They also say it was ported from PC Engine, but that might not be correct?
Psychic Detective vol. 3: Psychic Detective Aya
Psychic Detective vol. 4: Psychic Detective Orgel
RPG/graphic adventure. Also ported to SNES and 3DO, but not in English (?).
Quiz Scramble Special
The name pretty much says it all. I'm sure it's a lost cause if you don't speak Japanese.
Ranma 1/2: Byukuran Aika [Ranma 1/2: White Orchid Serenade]
A mix of story scenes (still pictures + audio dialogue) and...rock-paper scissors battles. Doesn't sound very appetizing, but might be playable for fans of the series?
Record of Lodoss War [Lodoss Tou Senki: Eiyuu Sensou]
Strategy RPG. Apparently playable without the language, especially for those familiar with the series; that, with a knowledge of katakana, may suffice. Featured in Left in Japan.
Romance of the Three Kingdoms III: Dragon of Destiny [Gekijoban Sangokushi III]
Strategy/historical sim in typical Koei style. Available in English on the Genesis/MD and any number of other platforms. Anything to recommend this one besides the Redbook audio?
Seima Densetsu 3x3 Eyes [3x3 Eyes: Legend of the Divine Demon]
RPG. Unplayable without knowing Japanese. Featured in Left in Japan. The soundtrack apparently has murderous saxophone. Review at Mobygames.
Beat-'em-up. Ported from Neo Geo. Fully playable w/o Japanese. Apparently a dreadful port.
RPG. Some say it's unplayable without knowing Japanese, but a knowledge of katakana can apparently go a long way. The Mega CD version is completely different from other platforms (including the Genesis). A translation has been attempted; current status unknown. Featured in Left in Japan. Here's a forum thread with a mini-review of the game and links to the romhacking.net project.
Shin Megami Tensei [New Digital Devil Story / Devil Summoner: The New Adventure]
RPG. Unplayable without Japanese. Supposedly much the same as the PC Engine version, and according to Racketboy there's also a Super Famicom version that's been translated. Featured in Left in Japan.
Sim game, ported in English to loads of other platforms (none of them Sega). Anything special about the Mega CD version?
Tenbu: Mega CD Special
Strategy/historical sim. Another Nobunaga game, but SegaBase has positive things to say about it. Probably not playable without the language.
Strategy/historical sim. Yet another Nobunaga game, but SegaBase has positive things to say about this one too. Probably not playable without the language.
Tokyo Mahjong Gakuen(not released, may never have existed)
Sega-16 user xelement5x has researched this game, and based on his findings it appears that it was never released. (Was it ever even a title in development?)
Urusei Yatsura: My Dear Friends
Graphic adventure. Allegedly playable without Japanese, other than not being able to understand the cutscenes. Also discussed a bit on Sega-16 here.
Warau Salesman [The Laughing Salesman]
Graphic adventure? Ported from MSX. Probably not playable without the language.
Racehorse management sim. Part of an acclaimed series by Koei; at least one other entry has been translated into English (for the Saturn), but not this one. Probably a drag without the language.
Collection of games, music videos, and other stuff for the WonderMega. Should mostly be navigable without knowledge of the language. Will this run on other hardware?
Anime FMV à la Dragon's Lair. Playable without the language, but you probably won't have more than a vague idea of what's going on.