Takashi Miike's rapidly expanding oeuvre includes something from nearly every genre (including a family picture and a musical?!). The Dead or Alive trilogy find him with his familiar Yakuza genre, but these films aren't your typical Japanese gangster flicks. Miike's style are all over these films. The opening montage in DOA1 is some of his finest work - eight minutes of rapid fire violence, drugs, car chases, assassinations, and death. Sergi Eisenstein would be proud. The ending is also particularly amazing. How to end a 100% insane yakuza ultra-violent movie? Miike finds the perfect way.
The films are a trilogy in name only. All three stories are completely different, but use the same leading actors. I haven't seen many of their other films, but it's my understanding (from reading Tom Mes's great book on Miike), that these are two of Japan's biggest action stars, working together for the first time. In DOA1, they're enemies. In DOA2, they're best friends. In DOA3, one of them is an android. All three stories are unique and all have interesting qualities. I would agree with the other reviewers that the third is the weakest, but I wouldn't go so far as to say it's lacking in quality. It's reminiscent of Miike's City of Lost Souls.
While the films are available separately, the three disc collection is definitely the way to go. They're all very good films and the first two are definitely among Miike's best work. Be sure you don't accidentally purchase the "R" rated versions. You want the unrated version with all of Miike's balletic, Peckinpahnian violence intact.
These films are known as action movies, but they all have fairly slow middle sections where the characters have time to develop and evolve. Whatever else he does, Miike always tells a good story. Anyone hoping for wall-to-wall action will be disappointed. However, those seeking a thoughtful action picture (or three of them in this case) will enjoy these films. If you think you know yakuza pictures, wait until you see these!