My current favorite would probably be Chihayafuru. It's about a girl named Chihaya who loves the competitive game of Karuta and holds it very dear as a bond between her and two childhood friends. The main character is interesting and unique, there is a good deal of character development among the cast, and the tournament sequences are tense and immersive. It was recently made into live action movies in Japan.
It's tough but my all-time favoritie would probably be Welcome to the NHK. It's simply brilliant and the closest visual media I've seen to Catch-22. One day a typical college student has a nervous breakdown. He becomes paranoid and shuts himself in his apartment. The stress and isolation lead to delusions that his life is spiraling out of control because of a conspiracy by a television station. Meanwhile, a mysterious neighborhood girl decides to "save" him. Turns out that she is just as mixed up and muddled as he is, however.
The series rides waves of hope and dispair, while the characters deal with addictions, depression, social disorders, and even suicide. Even more remarkable is that it can be flat-out hilarious one second and heart-breaking the next.
Childhood favorite? Maybe Ranma 1/2. It was fun and inventive.
