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Pani Poni Dash, based off complete randomness and it's an anime based off of anime/manga/movie spoofs (heck, they even got a Planet of the Apes spoof XD)
Azumanga Daioh, Pani Poni Dash, Excel Saga, Keroro Gunso, Konjiki no Gash Bell...that's all the recent stuff that would count as weird and good I guess.
Air is a very imaginative, but weird anime. I've watched the whole series and loved it, though I was left a bit confused by the ending. ^^; If anyone's seen the whole thing and can explain the ending to me...please do. XD
I also think Wolf's Rain and Cowboy Bebop are very creative anime series'. :3 They each have strong plots and awesome characters. =D
Oho...Paranoia Agent, hands down...non sequiturs in such abundance that it makes one question their own logical reasoning for ever deciding to watch...and yet, since it's horror randomness instead of comedy randomness, it ends up being rather unsatisfying.
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.