I'd say eliminate the cliches:
Human stupidity: Have less people walking backwards down a corridor, freezing in panic, not believing anything, turning against each other, etc. Instead, have people adapt to the situation and try to work together to figure out what to do. Resident Evil was good at this.
Slow/dumb zombies: I think the Borg from Star Trek make excellent 'zombies:' Obsessive, but by no means dumb--they adapt to situations, come up with combat tactics, and are tough in a fight. The raptors from Jurassic park are other good examples, if you'll allow me to stretch the definition. I've never seen it, but what I've heard of 'Tombs of the Blind Dead' has a great wrinkle: The zombies are undead templar knights who ride horses and track people by the sound of their heart beating.
Craziness: The optimist in me believes that not every group would have one person go nuts.
Evolution: Part of one of the points above, but it'd be intriguing if there were 'types' of zombies, a la video games. Maybe some zombies were 'workers,' others were scouts, some were fighters, and some were planners.
Just a few of my thoughts.