Adding in to the list of recommendations, let me tell you about this series I just finished watching - Gankutsuou.
A paraphrase of the famous book, The Count of Monte Cristo, it is a fantastic series that doesn't ever feel like an anime - and, in this case, that is a superb thing. Sure enough, it is not as memorable as the book - but that is pretty much the same thing as saying not everything is as hot the sun. Truly one of the best adaptations I've seen in a very, very long time.
Plus, the visual style, with its artsy use of the "unmoving plaid" technique, is truly dazzling. There are some people who find it annoying, but I, for one, was completely awed by it.