Simply put, zombies rule.
There's just something about a reanimated corpse, possibly your recently deceased good friend or relative, shambling towards you with blank eyes and outstretched arms, hungering to eat your brains and turn you into another undead, doomed to hunt for living flesh as well.
Zombie movies are practically a genre unto themselves. I think part of what makes zombie movies such good horror movies is their apocalyptic theme - the world is going to hell. They often a lack of a happy ending - even if the main characters survive, the world is usually still a very messed-up place. On top of that, the enemy is ourselves, both figuratively and literally, which can disturb us so much more than a completely inhuman monster.
The zombie movie phenomenon was started almost entirely by George A. Romero and his horror movie classic Night of the Living Dead (even though the term 'zombie' is itself never used in the movie; they did however use 'ghoul'). Many argue that this is still the greatest zombie movie ever made.
Here's the awesomely over-dramatic trailer:
NotLD came out before my time, but I did see it when I was pretty young and thought it was scary. Watching it again when I'm older really made me appreciate the brilliance of it. As a movie it has aged pretty well - it's still really freaky. Sure it may not be as flat-out frightening as some movies that came afterwards, but it set the standard and was the pioneering original.
Lucky for us, NotLD has fallen out of copyright and is hosted on Google video! So, without further delay, here's the full movie, Night of the Living Dead... They're coming for you, Barbara...
Night of the Living Dead (1968)
I stumbled across this site for this project, NotLD: Reanimated. It look like a pretty cool idea, they're taking contributions from different artists to recreate the movie. Props to them for using Creative Commons.
Here's their early teaser trailer: