Real zombies don't run.
"28 Days Later" was pretty good, though it does violate the slow Zombie rule.
Technically in 28 Days Later they aren't zombies they're sick but alive, though genrewise the movie fits best in the zombie apocalypse crowd (has more zombie movie flourishes than pandemic movie stuff, though the line between the two has always been pretty thin).
But that whole movie is made by the first 20 minutes, that whole "dead London" sequence is amazing.