IMHO, the best zombie movie ever. It's a 1992 film made in New Zealand by Peter Jackson, the same guy who later directed Heavenly Creatures. It has a priest who knows kung fu. It is also ludicrously gory

Don't rent this movie from Blockbuster Video. They carry it, but they cut out about 15 minutes from the fight scene at the end, which is really too bad, because that scene is awesome. You get to see zombies getting attacked with a lawn mower. At length.

I just went to the IMDB to get Peter Jackson's name, and I found out that the original title of this movie was Braindead. But everyone in the US knows it as Dead Alive.