10 ideas for tweaking zombies

Starting with a basic option: Headshots don't work. Maybe you need to take out the heart/other weak spot, or just destroy it entirely. 9 more ways of tweaking zombies in order to keep players from being jaded after the link.
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The players catch the occasional glimpse of a zombie who will eat other zombies. It's no dramatic affair- it simply walks up to a zombie and then seizes onto it. The "prey" will attempt to push them off and get away with typical zombie slowness, and the "predator" will usually overpower them and simply crush/break the body until it stops moving before it starts chowing down. It goes after the closest prey, zombie or human. Over time these zombies become more noticeable because they're more fleshed-out; their body type doesn't change, but their muscles are fully formed as though they were in excellent shape and died yesterday. It's not clear right away, but the more they eat the stronger they grow. They also regurgitate "hairballs"- half-digested hair, scraps of clothing, bone fragments, etc.
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Here's one that you don't give your players any exposition for: The zombies show basic stalking behaviors. They deliberately stop moaning when approaching an unspooked prey, will intentionally feign death, are more likely to remain hidden/inactive when the prey has the advantage in terms of numbers. . .this can just be an explanation for the use of several scare tactics, but the realization that they possess this sort of cunning can be quite disturbing in the right circumstances.
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The zombies possess varying degrees of clumsiness, and those that are often active seem to improve their coordination over time. The key is, those with better control over their bodies aren't moving like humans- instead, they're prowling about on all fours. They can't climb bare walls or anything fantastic, they're just. . .purer reflections of the inner feral nature that now dwells within what was once a person.
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For a larger thematic change: The zombies retain some of their past nature. Not exactly intelligence, mind you; more like a patient with a severe brain injury. They experience a limited degree of emotion and even some pain, will mumble to themselves and make the same idle gestures and absent-minded responses that they might otherwise. . .but when prey appears all that there is to be seen is a vaguely expressed mix of malevolence and desperate determination.
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The zombies are only predatory during the night. During the day, some are almost normal- most act in a confused and dreamlike fashion, not quite realizing any mortal injuries they have or blood on their hands. Start killing them then and they'll panic, scream, etc. And there are some who are so close to a normal person that you aren't sure whether or not they're still alive; maybe none of them are actually dead, it's just some mysterious curse that makes most of humanity into cannibalistic monsters when the sun goes down.
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At times, apparently corresponding to some sort of cycle, the zombies seem to have an urge to congregate at the highest or lowest places possible. For several days they'll climb trees (an awkward trail-and-error process, mostly error) and stand around on building rooftops doing what amount to king-of-the-hill to get on top of the ventilation boxes. The next week they've started massing together in culverts and sewers. It alters how survivors travel, and also allows for plenty of DEATH FROM ABOVE attacks- "Zombies fall. Everybody dies".
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The zombies' behavior varies based on the weather. During an overcast day they behave like a typical zombie's supposed to do. Sunlight agitates them, while light rain makes them quieter and more active. At night they're fairly docile, which means that the players will have to consider doing travel/errands during that time since you're a bastard like that. It's during downpours and thunderstorms that they go completely apeshit, smashing crap up and actually running after people. The rain makes it hard to tell who's human and who's a zombie, too...
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The zombies begin as docile. That is, all throughout the world the dead emerge from their graves and then do nothing but wander around, feigning death if they believe they're being observed. People are aware, it's all over the news; but there's just too many of them to immediately deal with each and every one, or even more than half. People are urged to stay away from the walking dead since they probably carry diseases. Some wonder if the zombies are migrating with a purpose. Whatever their reasons, something- a code in a radio broadcast, lunar cycles, weather (see above)- eventually makes the zombies go OM NOM NOM like normal. Can make for a very tense intro.
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The zombies are not hungry, but instead hate all living beings- animals and humans alike. They are driven to attack any living thing in close proximity. Perhaps they're attracted to heartbeats, or perhaps there's a supernatural cause at work- they can sense life forces, or some similar explanation. Either way, players see zombies attacking cats and dogs as well as people, stopping as soon as the battered victim has passed on.