In my mind, Zombies are generally simplified Humans. They have lost their human abilities and have become rotting robots. Therefore, they will devolve into their primal instincts, and go for their primary source of nourishment. Whatever that be, if it be human skin or flesh, then they'd probably attack themselves.
They wouldn't attack in packs because one of Human's first steps of evolution was to work as a group rather than selfishly, and if my prior statement is correct, then there would be a lot less singular zombies attacking you. Therefore, hordes of them would ultimately not happen, unless they were controlled.
The "BBBRRAAAIIINNNSS" stereotype would probably not happen as well, because if they were intelligent enough to know what specific body part to go after, then they would practically be humans with a terrible skin and brain disease (see: Ghouls via Fallout 3+)
Besides that, check up www.cracked.com for a full list of why a zombie apocalypse wouldn't last very long. The primary reasons are because the living cells in their bodies are... well, they stopped living, and there would be problems with that. If the temperature was too hot, then their flesh would rot and if it was cold, they'd freeze.