Dead Alive, Peter Jackson’s Magnum Opus.
Yeah, Dead Alive is a must see, I would say if you want to go down a list, review the Classics. Start with Romero's work, since he invented the Genre.
Night of the Living Dead, Dawn of the Dead, and Day of the Dead. The originals, not the later remakes. "Dawn" is what I feel is the single best picture ever shot in this genre.
Once you have seen the master define the genre, go and have fun. The
Return of the Living Dead pictures are a blast. Return of the Living Dead III is my favorite. Keep in mind this picture series is campy and fun, not as serious as the Romero pictures.
Also very funny is the British hit
Shaun of the Dead, and if you ever get a chance, the Australian picture
Cemetery Man is an underground classic that really deserves a shot. I could go on, but that is a good starting point,
Train to Busan is an excellent contemporary entry though.