Monsters Outside the Polis
Why are there so many monsters that are part human? One might argue that they represent aspects of ourselves that we find monstrous: desires, passions, even reason run rampant. In this setting, that is in fact how monsters originate. When a person goes too far in pursuit of his desires, he is transformed outwardly to reflect his inner monstrousness.
There are two kinds of monsters: monsters of passion and monsters of reason. A monster of passion has a human body but an animal head, such as a minotaur. A monster of reason always has a human face or head, such as a sphinx, and may even have a human torso and arms, such as a mermaid or centaur. Monsters of passion are not capable of speech, but make their desires plain through their actions. Monsters of reason are capable of speech and will quite readily explain their desires; however, they cannot be reasoned with as such and shown the error of their ways.
A monster of passion is driven to sate a bodily desire: for food, for sex, for rest (slothfulness), even for sensation. A monster of reason is driven to sate more abstract desires: for knowledge, for power, for glory/fame/reverence (worship), for possessions. Certain monsters already have historical associations: sphinxes with knowledge (riddles), satyrs with sexual lust, minotaurs with bloodthirst. Other monsters might require research into the symbology of different animals, or of course you could just make up something.
Monsters pose a dual threat to other people: they prey directly upon humans, but worse, their very proximity brings out the worst in others. Usually people are afflicted by the same desire as the monster - think of Bacchus inspiring the wine-and-lust-crazed Maenads - but their presence can also trigger the transformation in those who are already far gone in their own desires; only in this sense do monsters breed monsters. Thus, it is important that monsters be slain as soon as possible, lest they destroy the polis (city-state).
The characters, then, are monster-hunters - or heroes, if you will. Their goal is to discover the monster that afflicts the polis, determine its weakness, and destroy it. Naturally, as supernatural manifestations of evil, monsters have some immunity to normal weaponry and require something special to be slain, though that need not be a conventional weapon - in the classic case of the Sphinx, knowing the answer to its riddle was enough. Even with the proper bane, the characters must still be careful that they do not get caught and devoured, or worse, corrupted.
This probably could be run simply as a Dogs variant: the Pride, or hubris, of an important figure in the polis would cause some injustice, and the appearance of the monster would be the visible result, standing in for "demonic attacks." Those of you interested in that setup should compare with "Thunder in the Vineyard", an ancient Greece setting posted in the Forge. However, I do like the idea that the monster actually is the source of the evil and the true threat that must be confronted, not just a symptom of a regular person's failing; call it a more heroic take on the Dogs setup. Perhaps there's another game system that would be better suited, or perhaps it requires some new rules.