DoubleBear Productions has made an announcement about an upcoming zombie role-playing game set in the present day during a zombie apocalypse. The zombies will apparently be standard slow-type or "classic", but the real danger will be other humans. It is also noted that the game will be "open-ended", presumably meaning that there's not a central story line to be followed. If the game just went on forever without any goal in mind, though, that might get old kind of quickly.
Mokalus of Borg
PS - Side-quests would provide a big part of the story for the player, then.
PPS - I guess that would work.