I always hesitate to talk about what I think is "unique" as often times things that are thought to be unique often get revealed otherwise once we've been exposed to more that the chosen medium has to offer.
That being said:
Art - Bakeneko/Mononoke, hands down, has the most distinctive art that I've ever seen in anime. It's incredibly surreal, incredibly effective, and is (at times) beautifully animated. There's really not much else to say about it, because once you've seen that art style, you'll know what I'm talking about.
Story - Now this one is a lot trickier, since completely originality is nigh impossible to come by in any form of storytelling medium. If I had to choose, I would probably have to go with .hack//SIGN, mainly because I've never seen a franchise tie everything together quite the way that this series has, and SIGN gets props for being the strongest realization of the series' concepts.
As much as I love absolutely Mushishi, with its beautiful scenery and brilliant method of episodic psychological study (especially when faced with nature and other such uncontrollable events), I just don't feel comfortable saying it's the most unique I've ever seen.
On a more negative note, I must give a shout out to Dog Days, an anime from the current anime season. It has managed to take the concepts of war and consequence to a level of such utter absurdity that the only way I can describe it is as "unique."
