In a spectacularly good coincidence last week, Channel 4 had George Romero's The Crazies (1973) on, which I had heard of but hadn't seen before. The premise of the film is that a virus causing homicidal insanity has accidentally become loose in a small town in America. In a sense, what we have is a zombie film without any zombies.
Being made in-between Night of the Living Dead (1968) and Dawn of the Dead (1978), Romero clearly had very little money to spend on this, and it has that look that all low-budget 70s horror films seem to. What sets The Crazies apart from those films is Romero's more sophisticated take on the situation: the problem isn't so much the virus, but more the incompetent and heavy-handed response from the authorities.
I see from IMDB that an inevitable remake should be out next year. The core concept certainly has potential for a bigger budget remake, but I have a suspicion that, like the 2004 remake of Dawn of the Dead, the badly flawed original will remain the more interesting piece.