It's been a long time since I have watched the anime, but here's a quick rundown of some of the concepts I think the anime portrayed:
The resulting conflict, called the "Absurd," to find meaning and not being able to find any, at least, not in a humanely possible way. In other words, meaning can be logically found, but not be achieved. This concept is shown in Raul's mental breakdown as he slowly loses any possible source of meaning in his life. His adopted child, for example, could have been a source of meaning, but as he loses that and Pino, he began to create the Absurd and the way he resolves this is through suicide. The are other examples of the Absurd, more noticeable when they're talking about their Raison d'Etre. Others can handle the Absurd in a different way, particularly the Proxies because they're not (normal) humans, although those like Re-L was able to handle it as well in the end. The way Ergo Proxy portrayed Vincent's journey can also classify this work as an Absurdist Fiction.
For more: http://en.wikipedia.org/wiki/Absurdism
This is more broad and can be divided into two subcategories: dualism and monism or physicalism (also called Identity Theory). Dualism is where the mind is separate from the body and the latter is when the mind is the body. This issue is addressed when the robots begins to acquire sentience on their own. The Cogito virus, which seems to be immaterial, is what gives the robots in the series their free will, their "mind," similar to how dualism says that the mind is immaterial and separate from the body. Yet, the experiences each robot has is what makes them act different, which also depends on the body. The state of mind of an intimidating military robot is going to be different than that of Pino, where people are more likely to treat her like a child. This issue is also more notable between Ergo and Vincent.
For more: http://en.wikipedia.org/wiki/Mind%E2%80%93body_problem
The anime briefly touched on this, but it's there. The legitimacy of Romedau's government is questioned. Cities can be created and destroyed easily by the Proxies, so it seems that the council is very powerless. More than that, no one voluntarily enters these cities. Rather, people are forced to exist inside them, either through artificial birth or through emigration (they were either to die in the harsh outside environment or live inside). In contrast, the commune outside of Romedeau works the opposite, in a way. Thus the problem: would you be willing to give up some of your freedom for comfort or would you rather have complete freedom?
For more: http://en.wikipedia.org/wiki/Social_contract
Very similar to absurdism. This problem is the question of where meaning comes from, if there is at all. It also deals with the issue of where existence came from, whether we existed without our bodies and how does it relate to our meaning. Existentialism on its own is too broad, however, but it seems to me that the anime touched on this as well.
For more: http://en.wikipedia.org/wiki/Existentialism
There's a lot of references on the other hand, so I'll only list a few:
Utilitarianism - Society should be guided so that everyone is equally happy. Thus everyone in Romedau is given meaning.
Transhumanism - There was a scene where a city is run completely by robots. This seems to be more of a jab on transhumanism rather than a support for it, as it shows there's no need for humans if everything is mechanized.
Divine Command Theory - Whatever the council says, it has to be good. Why? Because they said so.
Übermensch - Nietzsche's idea of a perfect human and how human propagation gives meaning. The proxies aren't perfect, but it somewhat alludes to it considering how obscenely powerful they seem to be and that their mission is to perpetuate human society, if I recall correctly.