Yakuza 0

Yakuza Kiwami

Yakuza Kiwami 2

Yakuza 3 Remastered

Yakuza 4 Remastered

Kurohyou: Ryu ga Gotoku Shinshou

Yakuza: Dead Souls (non-canon)

Kurohyou 2: Ryu ga Gotoku Ashura Hen

Yakuza 5 Remastered

Yakuza 6: The Song of Life

Judgment

Yakuza: Like A Dragon

Like a Dragon Gaiden: The Man Who Erased His Name

Lost Judgment

Like a Dragon: Infinite Wealth

Like a Dragon: Pirate Yakuza in Hawaii

Yakuza Kenzan! (non-canon)

Like A Dragon: Ishin! (non-canon)

While the Judgment series is a standalone and Judgment contains no spoilers to the main series, Lost Judgment is a continuation of a specific event from Like A Dragon and should be played after it.

Ishin!" is disconnected and can be played at any time, but given its status as a fanservice game, it's best played after Like A Dragon.

If you have access to Dead Souls and plan on playing it, it came out between Y4 and Y5 but is currently exclusive to the PS3 unless you plan on emulating it