This is something I used to have a big interest in, and posted about before on a few other forums. In my own opinion, I think the gods are very varied, and that the morality of one god may be very different from that of another. However, I also think that that doesn't necessarily mean the gods will share the moral principles of the human beings of this age or a specific culture, even if that god was once human (since moral principle seems to change slightly over time, and the specifics seem to develop and evolve throughout human history). Then, there is also the thought that the gods may be amoral, but may sometimes 'mimic' human morality in order to interact with humanity or to appear more approachable to humans of whom they wish to interact with. I also like to draw a line, personally, between amorality and apathy, but this is my own opinion and experience.
What are your opinions and experiences on the matter? Feel free to challenge my opinion - I only present it with the hopes of kicking off the discussion.