Depending on what kind of zombie you are talking about depends on if or more relevantly, how you can kill them.
If its a virus, such as a mutated mad-cow (which would be the most likely option, as it would produce the best 'zombies') than its just their decision making/personality and motor skills are altered, and they never actually died. Therefore, killing them would be just as easy as killing a normal person.
If they are undead zombies, such as something like the T-virus (I wont count zombies that are reanimated corpses by magical means) that reanimates previously dead bodies, than it would mean that you just need to separate their brain from the rest of the body. In the case of the virus taking over the whol body and operating each part of it independently from the brain, than you need to torch the body or sever all its parts.
So actually, yes, it is possible to kill zombies. You just have to do the right thing for what kind of zombie. Torching or blowing up the zombies is obviously the best way to do it, as without a body, it doesnt matter what kind of infection/virus/magical means it is, if there is no body, there is no zombie.