I'm toying with the idea of adding a fourth option to alignment selection for characters (including monsters and NPCs) - unaligned. In the Classic D&D rules (and also Labyrinth Lord) there are 3 alignments - Law, Chaos and Neutrality. Neutrality has often been assumed to be when you don't really care about either Law or Chaos, but it is also chosen by those who don't want to be tied down to either Law or Chaos.
With the system I'm proposing, unaligned PCs, NPCs and other creatures would be essentially uninterested in the battles between Law and Chaos. In the case of monsters this may well apply to those who are not intelligent enough to have ethical behaviour, including most animals, vermin and some constructs. Unaligned creatures may show signs of chaotic or lawful behaviour or even both but they do not consistently act that way.
Neutral characters and creatures are what might be described as "consciously neutral", in that they strive to maintain balance between Law and Chaos at least within themselves, and perhaps in the wider world. Neutral NPCs may be deliberately careful and stand-offish about getting involved in other folk's disputes. They may work for a neutral deity or another force of neutrality (druids, if they exist, would be a good example). Neutral creatures tend towards moderation and don't pick unnecessary fights, but also are not so concerned with justice, mercy and loyalty as those who follow Law.
In my house rules, white dragons, stone giants, wereboars and centaurs are all unaligned, while blue dragons, cloud giants, weretigers, pixies, dryads and gnomes are all Neutral.