Coolness! Well I personally prefer zombie games like The Walking Dead where you have to make tough decisions, to games where it's mostly running around killing things, so some interesting situations would be:
Two survivors are both getting attacked by zombies and you only have time to save one. The other dies.
A person you really care about becomes a zombie, and you have to kill them.
You find a child survivor, but they make loads of noise and won't stop crying, and they're drawing the zombies attention. You need to figure out a way to make the child stop screaming, or kill them before the zombies get you.
One of the zombies still seems to display some sign of human intelligence and emotion, and you have to decide whether to kill it or try to communicate with it. If you decide to spare it, the zombie gradually becomes more aggressive and depending on future decisions, it either kills you, or sacrifices itself to help you get away from other zombies.
With zombies running around everywhere, there's no law enforcement, so it's not only zombies you need to worry about, some of the survivors are dangerous too, and would happily kill you for a packet of animal crackers.
Romance is always a nice addition to a game. Maybe you meet a lovely young girl who you fall for, and the pair of you could live happily ever after... Or she could die tragically at the end. Either's good.
That's all I can think of so far. Remember, if the game's got a lot of characters, you should try to make them range in age and race, and have roughly the same amount of female characters as there are males. Also try to get some creepy little kid zombies in there! Nothing scarier than an adorable little kid that gets turned into a zombie 