If you're looking for anime similar to FLCL, you might like these titles. All recommendations are made by Anime-Planet users like you!
Takao Kasuga is a lonely boy who spends his days immersed in books to escape his frustration with life. His only source of joy is the beautiful Saeki, who he secretly admires from afar. However, Takao's obsession goes too far one day when, in a moment of emotional folly, he steals the girl's gym clothes and takes them home with him. Worse, his terrible deed is spotted by Sawa Nakamura, a mysterious outcast who sits behind him in class who threatens to reveal the boy's secret unless he promises to engage in a contract with her. At first it seems Sawa just wants some companionship, but soon it becomes clear that this "contract" involves more than mere afternoon chats. In fact, Takao is about to discover just how dangerous his bond with Sawa is and how it threatens to tear everything - his life, his love, and even his sanity - apart.
Although these shows are very different in tone (Flowers of Evil is slow-paced and creepy while FLCL is manic and ridiculous), they're pretty similar when it comes to themes. Both feature a young teenage boy that hates the place that he lives in, struggling with growing up. Both protagonists have their problems increase when a strange, perverted girl enters their lives. Also, both series have a lot of experimental animation.
I can't garuntee that fans of one will like the other since the difference in tone is pretty significant, but I think there's a chance that if you like one you might be interested in the other.