[Kotohono]

If you want a great, weird, original, and mysterious anime then you definitely want to watch Bakemogatari, my opinion was best series out of 2009, and it fits all those words. Also if you enjoy I'd highly recommend Katanagatari as it's same author, but vastly different setting, though similar in dialogue heavy nature.

And I'd say B Gata H Kei is a rather original, hilarious, and recent romance series.

Also I'd second to Angel Beats, or Haruhi Suzumiya 1.5