1. Elfen Lied - For it's violence, affectual story regarding character relationships, and mature themes throughout. The ending is extremely hard hitting, and i dare anyone to watch it and not be moved. A short and sweet story that burns itself into your mind.
2. Chobits - For it's suprising maturity in dealing with character relationships. Particularly in dealing with the awkward love between a man and a woman when the woman is not 'real'. Underneath its light-hearted surface it tackles some pretty tough social issues and is very emotionally affecting.
3. Spice and Wolf - A very clever economic-drama, with light romantic themes. Lawrence is a shrewd merchant, and you may find yourself suprised in how much you get involved in his travels and the way in which his trade works, with Horo providing a stark contrast to his serious side with her sarcasm, wit and humour.
4. Inukami! - Who doesn't love a good Ecchi, right? Far less mature than the aforementioned, this one does not take itself seriously. A perverted man with women who are 'fox-goddesses' known as Inukami is a setting for comedy and some outright embarrassing moments, you can get a good laugh out of this one.
5. Escaflowne - Now, i don't remember much about this anime. Only that i saw it as a child when i was very young and used to sneak down to watch TV at 11pm, before the kids' network took it off the air. What i do remember was a man being somehow 'connected' to his giant robot, escaflowne, a corporation or army that was out to kill him, and von being some kind of angel. For what it's worth, this one deals with violence, power struggles, and a dash of romane that never really takes the centre theme but helps to accentuate the ideals of the story along.