Not only did the movie revolutionize the horror genre but it also introduced the modern concept of the slow moving zombies, portrayed as the undead horde who feast on the living with an explicitly large amount of gore.
That also makes it a must see for all zombie lovers. Although it’s been remade twice, with the 1990 version (which is ok) and the 2006 3D version (which is not as good), you should still start with the original.
Being more than 40 years old, Night of the Living Dead is in black and white and it's easy to see it was originally a low budget movie. This makes it a little less scary by modern-day standards, but the claustrophobic and tense atmosphere of survivors make their way to an abandoned farmhouse and particularly the scenes showing some parents deciding to hide in a basement with an infected girl are memorable.
As a final note it’s also worth noting that the original Romero movies show subtle political references to the Vietnam war, and the final scene makes a statement about the racial tension at the time of the movie’s making.