All questions about shot placement depends on how the zed was created.
1. Disease: 28 Days/Weeks Later, As we've discussed in the Biology section, it is impossible for a disease to re-animate a corpse. Therefore, all disease-based zeds are still alive. Shoot for the head. If you don't have good aim, go for the chest. If it will kill a human instantly, it will redead. These are the most likely types of zombies
2. Organism: Las plagas or goa'uld anyone? Unlikely as they may be, they can be tricky to kill. You have to finish off the organism to finish of the zed. Where is the organism? Likely the brain (Boom, Headshot), or the spine (high calibur to the chest or shoot them in the back).
3. Technological: Borg, Replicators. Good luck... Uh, I guess shoot the control units or blast a hole in their chest. EMP is a good move though, if they aren't shielded. Fun times if they are... Melee weapons worked well on them in TV media, though.
4. "Hell Filled Up" Paranormal: All those "- Of The Dead" movies. Take out the head, or use the high calibur stuff to blow a huge hole in the chest.
5. "Lolwiccan Summons Demons" Paranormal: Army of Darkness. Sorry, you're kinda boned. Just taking out the body's communication lines won't do a thing. Body parts will animate on their own. Explosives are a must. Since magic obviously works in this model... I'd put on my robe and wizard hat, and magic missile that crap.
6. "People Become What They Really Are" Paranormal: No examples. Basically, some effect turns people into something smiliar to what they are in their personality. So people who live their life just stumbling about and without any point but to eat, drink, and keep existing? Zeded. See disease based or "Hell Filled Up" for tactics.
Hope this helps.
"I think, therefore I am" - René Descartes
"What I think defines what I am." - Rezz