I find zombies interesting on an intellectual level. The slow, mindless one that have to bite you. (Read [The Zombie Survival Guide](http://www.goodreads.com/book/show/535441.The_Zombie_Survival_Gui de) for more info.)
Zombies are interesting as technical and coordination problems because killing them is straightforward and can only be done in a limited number of ways. Therefore, optimizing how to kill them is simple. Just go for the head. Then the question becomes, "how do I destroy the most heads for the least cost and effort?". That's one hell of an engineering problem to think about.
As a coordination problem, zombies are pretty trivial if people don't panic and remember to just hit them in the head. After all, zombies are slow, obvious, and have no tactical ability. A well organized group of people could go so far as to take some humans, put them in a secure cage in the middle of an open area, post themselves up on buildings, and snipe any zombies that come nearby. At the end, airlift the cage out with a Chinook.
Personally, I think the most effective approach is to set some sort of bait and then bombard the approaching hordes of zombies with flak, which is pretty much guaranteed to shred their skulls. Any zombies that make it through the bombardment can be picked off with sniper fire. Since zombies can't really climb, you could post snipers on something like a grain elevator with the ladder moved up. It gets too hot, airlift them out. After all, zombies can't fly.
However, people do panic all the time, since nothing speaks to human fears like an enemy that can violate conservation of energy. The lack of susceptibility to any damage besides head injury is also unnerving. Also, people find it hard to kill infected family members. If they didn't, the infection would end down pretty fast. After all, the initial base of zombies would be small and easily removed, probably by military personnel who could keep it together long enough to shoot them properly. Any infected would be promptly killed by sad family members or nurses, and the infection would die down there and then.
I'm impressed by how well researched World War Z and The Zombie Survival Guide are. Max Brooks really does know his stuff.
Zombies are also interesting because whenever you imagine a post-zombie world, you're not one of them. You're one of the survivors, even though that should be unlikely. But hey, everyone likes to dream. And then it becomes a story about living life in a world without rules. Some social consequences still apply if you happen to live with other survivors, but that's another interesting topic for another time.
On a side note, the website Zombie Go Boom has an impressively large selection of weapons tested to kill zombies. I think Max Brooks really nailed it with the Lobotomizer, a cross between a shovel and an ax. It just looks like the right tool for crushing a skull. Even watching someone swing it just looks, well, satisfying.
World War Z also gives an unusually poignant view about humanity. It portrays everything from a general ordering half of a nation's death, and then killing himself, to a hikikomori vowing to live a better life after narrowly escaping death.
It also gave the best description of America's ethos that I've ever read.
We don't have the luxury of old-world pillars. We don't have a common heritage, we don't have a millennia of history. All we have are the dreams and promises that bind us together. All we have... All we have is what we want to be.