I just got finished watching
Haibane Renmei today, and I just had to mention it. That's the best five hours of TV I have seen in a long time. It's about this race of angel-type creatures with grey wings called haibane. They live in a walled city called Glie, which is a human town that basically exists for the haibane. The haibane had a life (presumably as humans) before they were born in that form, but nobody can remember what happened there. A haibane girl named Rakka is born from a cocoon one day, and the series is basically about Rakka coming to understand and live in this new world. It's a really fascinating and touching story that goes from being wonderfully happy at some parts to very sad at others. The pacing is very deliberate, so you really get to appreciate the detail of the show's world and characters.
It's not really a new series, so some people may have already seen it, but I haven't watched a lot of anime shows since I was 18, so it's new to me. It was such a refreshing change from most of what I see on TV, I thought somebody else might enjoy it too.