Big O is a philosophical anime about memories and their representation. Really understanding it requires several viewings. It's not obvious, for example, that the mecha in this anime are symbols of ideas/movements/memories. It's even less obvious how to interpret them. The stories in each episode are merely the surface.
The story is unusual. On the surface, it may even seem corny. Paradigm city, a city where everyone lost their memory 40 years ago? Certainly sounds something like B grade Sci-Fi. But if you're like me and you like unusual plots, this is definitely one to watch. Otherwise, just give it a chance.
As I said in the introduction, the stories often feature details that are not easily noticed or understood. You may need to watch it more than once. There are admittedly some loose ends in the story, but not too many.
The anime is unusual in that it looks like the Batman cartoon. Apparently this studio had a hand in animating Batman. Other than giant robots, it does not look like your generic anime.
The opening and closing songs aren't great. However, the sound score is outstanding! The show features a mixture of orchestra, jazz and electronic. Many of the songs are quite stunning. The sound score quality is certainly unusual for anime (at least those that I've seen).
It's worth noting that having seen both the sub and dub that the dub is pretty good. In fact, I recommend you watch the dub.
The characters are well developed and generally consistent throughout the story. I found Dorothy to be the most likeable and memorable character, followed by Norman (the butler) and Roger (our main character).
I found this anime to be extremely enjoyable. Having seen season 2 on Adult Swim, I was compelled to purchase Season 1 on DVD (I also bought Season 2) just to watch it. But it did take a few episodes to find it so interesting.
This anime is great! It's jam packed with details and ideas that require some thought, great characters, and a curious story. It's definitely something you'll want to watch again and again.