A young couple goes to Haiti to get married. They are extended an invitation from a local millionaire to come over for dinner... turns out he's obsessed with the girl and is conspiring to steal her. The millionaire hires Murder Legendre (Bela Lugosi), who has hypnotized half the population into being his zombie slaves to work in his factory, to use his powers over the girl.
It didn't dawn on me right away, but now I think White Zombie is a racial description. Legendre's zombie slaves are all black Haitians, so when he turns the girl into a zombie slave I guess that makes her the white zombie. So it's not just a cool sounding title.
Whatever problems White Zombie has due to its age and independently financed budget (some bad acting and dialogue, corniness), they are largely negligible. The film is heavy on atmosphere and even genuinely creepy in places, its under plotted story is glossed over by its nightmarish ambiance. I've been guilty of not always giving a fair chance to horror movies this old, but let me be clear that this is one of the good ones.