Contested Sequel: Fans are split over whether TGM3 is an improvment upon TAP with its improved Arika Rotation System (specifically, the new "floor kick" added to the I-piece to make it easier to rotate when in 20G and the piece is horizontal), or Fake Difficulty: The Game due to the COOL system resulting in an unreasonably fast speed curve and the Easy mode having unintuitive and guide-requiring scoring mechanics.
TGM ACE has an awesome remix of "Katyusha", heard only in Another Road.
Cult Classic: Although the series is known through memetic videos at best outside of Japan, it does have a small dedicated following in the West. This seems to be changing in 2015, as demonstrations of it at Awesome Games Done Quick have helped bring more exposure to Western gamers. In Japan, the Pier21 arcade in Kodaira maintains a dedicated set of TGM setups, with periodic competitions still being held for the games over 15 years after the original TGM was released.
Default Setting Syndrome: World Rule in TGM3, particularly amongst those who haven't played any of the TGM games prior to it.
Friendly Fandoms: You can expect a lot of TGM players to also be Bemani or shmup players, most likely because all three of these comprise challenging skill-based single-player arcade games.
Mainstream Obscurity: The game has seen a lot of positive reception from Western fans...the problem is that few play it, partly because for most Westerners, the only way to play is to be lucky enough to live near an arcade with it (of which there are very, very few), buy the arcade hardware for a non-trivial amount of money, play clones, or pirate it.
Memetic Mutation: Drift-compatibleExplanation TAP in Doubles Mode requires a very strong degree of cooperation between both players, leading to jokes, especially during Doubles exhibitions on Awesome Games Done Quick where people make jokes about the players being "Drift-compatible", a reference to the mind-linked Humongous Mecha pilots in Pacific Rim.
Mis-blamed: It was believed that TGM4 was canceled due to the Tetris Company's meddling, but it was revealed on December 5, 2010 that Sega refused to publish it and that Henk Rogers and the Tetris Company actually like this series. There are still some details left to speculation, but the troubles related to clones are no longer the only point of contention.
Most Annoying Sound: The REGRET!! sound in TGM3. Not only is it an indicator that you're going too slow, but it also means you've just lost one grade.
20G has appeared previously in an obscure Tetris clone for the Sharp X68000 computer known as "Shimizu Tetris".
For the more astute Tetris players reading this, the rotation system and piece colors for the TGM series is the same as the one in Sega's 1988 version of Tetris, only with the ability to rotate in more than one direction, and a mechanic that shifts the current piece to the side if you try to rotate it but normally can't due to a wall or piece obstructing it.
Firm drop for some players, which has led to many a misdrop (and is possibly why players in some regions stick to World Rule, which offers standard hard drop).
In the original TGM, allowing and refusing VS matches can only be changed through operator settings; if they're disabled, both sides can peacefully play single-player but can't battle, and if they're enabled and another player has the lack of etiquette to put in their coins and press start, the first player's run will be ended. Subsequent games allow the player to refuse VS matches simply by pressing their start button.
Sequelitis: TGM ACE. A good Tetris game, but you'd be hard-pressed to find someone who would regard it as a great game by TGM standards.
Signature Scene: The "invisible Tetris" sequences in the second and third games that are triggered by fulfilling certain difficult criteria.
They Changed It, Now It Sucks: TGM4's version of the Arika Rotation System would have had, instead of step reset (in which the timer for a piece locking resets only on a piece moving down), use move reset (in which you only need to move the piece). This has not sat well with some fans.