This was a difficult one to decide. I have many favorites. But, if I must choose one, then I choose:
Princess Tutu. It is an anime fairy tale, with themes from other fairy tales, poetry, opera, and ballet. As a musician appreciative of the fine arts, I really enjoyed the concept of the show, the plot, the characters, and the impressionistic style. It is a must-watch for every human with access to first-world technology.
Cowboy Bebop. I must say that I do enjoy science fiction. This one blew my mind. Not only is there action and drama, there are tons of scientific "yet-to-bes" for me to mull over in my mind and wish existed. Couple that with awesome music courtesy of Yoko Kanno and the Seatbelts and a successfully-fitting aesthetic, and you get one spectacular show.
Honorable mentions: xxxHolic, Miyuki-chan in Wonderland, Higurashi no Naku Koro ni, FMA: Brotherhood, Kanokon, Chihayafuru, C, Death Note.
Tomorrow's prompt: "my anime crush"