I'd have to say FLCL, because of it's randomness. I had to watch the series over a few times to understand some of the things they said. This may only be because I was tired and it was 3:00 in the morning, but it's random anyway.
Another is probably Kaleido Star, but I don't know how many of you have seen it. The plot is pretty creative, and some of the things that happen in it are random. Like the little guy that floats around and talks to Sora, for example. He scares the crap out of her. Her dreams and ambitions are different than the normal anime, where it's all about "fight this" and "kill that" or "Gundam Suits". I really liked it.