Fan Translation: A few of the Madou Monogatari games, the Famicom Puyo Puyo, Super Puyo Puyo Tsu, the PC version of Puyo Puyo SUN and the DS versions of Puyo Puyo 15th Anniversary and Puyo Puyo 7. A translation of Fever 2 has been in progress for at least three years, while the effort to translate 20th suffered a major setback in the form of a server crash.
Keep Circulating the Tapes: The English arcade game. Not only did a bootleg version make it to MAME first, it apparently took four more years for a legit version to be tracked down and dumped. (This might be the reason why the English game's authenticity is called into question.)
Surprisingly, this doesn't apply to Madou Monogatari 1-2-3, which D4 Enterprise has distributed for PC. All bets are off on any other Madou Monogatari games, especially from Discstation.
No Export for You: Every game except the Dolled Up Installments, the Neo Geo Pocket Color port of Tsu, Puyo Pop on the GBA and Puyo Pop Fever. The English version of the first arcade game could potentially be another exception. The Mega Drive port of Tsu is available (untranslated) via the Wii's Virtual Console.
Inverted with the N-GagePuyo Pop, which was released everywhere except Japan.
Port Overdosed: The first arcade game and Tsu, with Tsu being the biggest offender. For example, the two games' Mega Drive ports and original arcade versions are available on the Japanese Wii Virtual Console, despite the fact that their arcade hardware was essentially a Mega Drive with extra sound capabilities. (To be fair, the arcade ports are online-enabled...)
Puyo Pop Fever is only a port or two shy of reaching this status.
Unsurprisingly, the Dolled-Up Installments pull assets from the original Puyo Puyo. An especially-amusing example is Kirby's Avalanche's title screen: if you look closely, you can see "PUYOPYO" [sic] written several times in the background.
Many of Puyo Puyo's sound effects, particularly the "serious" effects used in the first two games' respective Satan battles, were first used in M.U.S.H.A.
The vocal clips were taken from Madou Monogatari 1-2-3. Becomes obvious when you find out that Ruluelacks a catchphrase.
The English arcade game recycles voice clips in instances that the Japanese game did not. This may be related to space issues, as two voice clips (both of which are used in the Curtain Call) are cut entirely.
Puyo Puyo CD Tsu features the pre-battle cutscenes from the Saturn and Super Famicom ports as an unlockable...except that they all take place in the "meadow" featured in the first game.
Sequel First: Madou Monogatari 2 was actually the first game in either series to be released anywhere. A beta version was included in the Christmas '89 edition of Discstation.
Whatever game that you consider to be the first Puyo game to be released internationally (arcade translation, Mean Bean Machine, or NGPC Puyo Pop) definitely isn't the MSX or FDS game.
The Western world didn't receive a Madou Monogatari game until 2013.
Talking to Himself: While this is to be expected of the earlier games, even now there are a few examples. We have Arle and Klug and Yu and Rei (being twin siblings) to name some.
What Could Have Been: The very fact that Puzlow Kids exists implies that Compile and/or Sega were trying to find ways to bring Puyo to the West, before giving up and deciding to re-skin the game. According to one of the Japanese guidebooks for Tsu, Compile was going to try to get Super Puyo Puyo released overseas before they were approached by Nintendo for Kirby's Avalanche.
Super Puyo Puyo was apparently going to have the Offset mechanic and Hard Puyo; however, Compile decided to save them for the sequel.