Kiryu doesn't kill. Explanation Although Kiryu has Thou Shalt Not Kill as part of his moral code, fans have a field day pointing out the many things he does that should prove otherwise, such as using a gun in the car chase shooting sequences, using a waiter as a human shield in the first game, or heat actions that would easily kill someone in real life, such as throwing people off buildings, shoving nails into their mouths and many more. This meme is often coupled with the infamous twist in Yakuza 4 and you get people talking about "rubber nails", "rubber knives", and "rubber explosions" to explain away his definitely-not-lethal escapades.
KIRYU-CHAN! Explanation A phrase Majima says whenever he encounters Kiryu. This reached a peak with Yakuza Kiwami, with the Majima Everywhere system basically making this Majimas catchphrase.
Waiting for localizations Explanation It usually takes a while for Western releases of the Yakuza games to release. The Remastered Collection was a big example of this, with the remaster of 3 releasing in the West after the whole trilogy was released in Japan. Up to Eleven with the Kenzan and Ishin games, which have received the No Export for You treatment for years.
Kiryu will never get into Tekken 7Explanation Kiryu has been a big fan request for Tekken 7 as a Guest Fighter. Sadly, that has not happened. This meme reached a all time high when Negan was announced as a DLC fighter.
24 Hour Cinderella Explanation One of Majima's karaoke songs, which became popular due to how absurd the Imagine Spot sequence is compared to the rest of the gane. The scene got many people hooked on the game.
Sagawa drinks piss Explanation Sagawa at one point makes a off-hand comment that he drank urine. Yakuza fans had a field day with this one.
Majima Everywhere Explanation People had a field day with the announcement of the "Majima Everywhere" system and photoshopping him into other completely unrelated series. When you consider the kinds of places Majima will actually show up in Kiwami...
Kiryu kicking the door open Explanation Just before fighting Shota and rescuing Date from him, Kiryu kicks the door open which sends a mook flying. It really caught on, due to the whole ridiculousness of the whole scene.
Kiryu slamming the desk Explanation A video clip of Kiryu banging his fist against a table in frustration after learning that Sayama is going after Ryuji on her own, which got a life of it's own, with people using it to convey shock upon learning about sex or racism.
Ibuchi is Dio Brando.Explanation The Jojo References came flooding in once fans learned that Kei Ibuchi and DIO shared the same voice actor, Takehito Koyasu
RUBBER BULLETS Spoilers It's revealed that Saejima actually didn't kill anyone in the Ueno Seiwa hit because his guns were actually filled with rubber riot bullets. Considered one of if not the biggest Ass Pull in Yakuza history, it's become a two-word summary of the goofier aspects of Yakuza 4's story. It's also invoked as a tongue-in-cheek explanation for the more nonsensical aspects of other completely unrelated plots in Yakuza or the surprisingly low canon killcount of the protagonists. Sometimes substituted with other words (e.g. "plastic projectiles" or "elastic munitions", or with "bullets" replaced with other things like "fists" or "helicopters" as appropriate).
Like A Dragon: Like a DragonExplanation The inclusion of the Japanese title in the English version brought on a few jokes about redundancy.
Yakuza: Like A Dragon QuestExplanation A combination of Dragon Quest getting name dropped in the trailer (complete with the revelation that Sega even got permission from Square Enix to do so,) and the game being a turn-based RPG.
Japanese Eric AndreExplanation More than a few people noted that Ichiban's afro makes him look like a Japanese Eric Andre.
Yakuza KartExplanation One of the new minigames is a straight up go karting race. Fans had a field day comparing it to Mario Kart.