Dawn of the Dead (1978) - The classic zombie movie, and for good reason. Has everything a zombie movie needs.
Day of the Dead (1985) - A worthy successor to Dawn, and features Rhodes, one of my favourite all time villains.
Zombi 2 (Zombie in the US) - The unofficial sequel to Dawn of the Dead, Zombi 2 is in Italian, but is worth watching for the scene where a zombie fights a shark. And it was a real shark with a stuntman. Insane.
Wild Zero - Japanese people enlist the help of a local punk rock band to fight the zombie apocalypse. As you do.
Dead Set - Not strictly a movie, but worth checking out for the social commentary about reality tv and it's effect on the public, and to see Davina McCall get what she deserves.
Dawn of the Dead (2004) - I'm including this, because it's one of only a few remakes I consider to be successful. It has enough elements of the original in place, while managing to be it's own film.
White Zombie (1932) - Absolutely awful, but the first zombie film ever made, so had to be included.
Shaun of the Dead - Funny and a legitimate zombie film. I hope Zombieland manages to be as good as this.
28 Days Later - Not a zombie film, but Danny Boyle's horror manages to pay homage to zombie films of old while updating the formula enough to make something captivating and original.