Neon Genesis Evangelion
Neon Genesis Evangelion is a Gainax work like The Wings of Honneamise, and Otaku No Video. Evangelion is more disturbing than either of their two earlier works. It was made as a television series, 26 episodes. It's a giant robot tale of sorts, but it is not as straightforward a storyline as something like Patlabor. The robots, called Evangelions, are piloted by teenage pilots. Don't expect Top-Gun type pilots. Maddness, loneliness, depression surrounds the pilots and everyone working around the Evas. The story is rife with strange biblical and apocryphal references and images. This is one of my favorite animes for it portrayal of the way people isolate themselves from one another in a world decimated by what might be God. The final two episodes were so confusing and non-conclusive that they released two movies as followup.Oh, by the way, the movies are even more confusing than the TV shows, but they're great fun in a mind-bending way.
A great thing about Gainax is they don't feel like they have to spell out everything. If you like everything to make sense, you'll probably get irritated by NGE, but try to think of the confusion as how the main character, Shinji, only fifteen years old sees the world.