A brilliant anime indeed. I think that this show starts off well, in that the first few episodes give us a good insight into the personalities of some of the characters. These personalities are more and more revealed as the show goes on.
The main thing that the show deals with is memories, and how these memories can effect people's lives. In the world of Big O, a catastrophe happened 40 years ago and everyone lost their memories. Some people allow their destiny to be governed by their memories which a few people in Big O do. One of my favorite things is that memories are treated as an actual object, in that memories can be captured and also destroyed by people. Of course, Big O is an anime with giant robots, some people say that they don't really contribute to the show that much however. I think that Big O could have been just as good without them, but I still think that they contribute to the show.