Night of the Living Dead, Dawn of the Dead and Day of the Dead. Don't watch the crappy remakes. Watch the original Romero versions. The Night of the Living Dead remake is not terribly bad, but still not as good as the original. Also, any of Lucio Fulci's zombie flicks.
Most modern zombie flicks are just awful, with the exception of Zombieland. Zombies went from being a docile, barely mobile but slowly building threat to being super-hyped ultra monsters that were LESS agile when they were alive.