I know that for some in any anime we can learn things... but there are some that just deeper.
When I've watched first Gundam Seed, I was surprised to see how war was presented with both points of views of the war...
In .Hack Sign, we could think about the MMORG relationships or just the net ones. How can one be sure the other said the truth ? Don't you wear a mask on internet ? About the trust ?
Chobits can show about the importance of computer science. Is spending time with a computer even as cute as Chii is as worthwile than spending it with a human being ?