Zombi 2, Zombie, Zombie Flesh Eaters, Zombi.
Call it what you will. This 1979 movie by Lucio Fulci may not be the best zombie movie ever made, but it is worth a look. At the very least, watch the underwater zombie-vs-shark scene (with the actual shark trainer as the zombie; a last minute casting decision when the original stunt actor was unavailable the day before the shoot. Coincidence?). You can watch a clip of it further in this post.
I could go into more detail about the different titles this film went by around the world or what to expect in terms of plot, but Tim Brayton over on "Antagony & Ecstasy" does a great review with loads of information.
And don't go looking for Zombi Part 1, because this movie isn't actually a sequel. There just happened to be another movie out at the time called 'Zombie', so to differentiate it, they called it part 2. Because that's less confusing. Apparently.