Another great one is 'FLCL'. It's a really unique and wild anime. It has a very distinct art style and a story that's full of energy and quirkiness. There's no manga or light novel it's based on. It's all about this strange boy who gets involved with a mysterious girl and all kinds of crazy things start to happen.
'Samurai Champloo' is also an anime not based on manga or light novel. It combines elements of hip - hop culture with a samurai - era Japan setting. The story follows two samurai, Jin and Mugen, and a girl named Fuu on a journey. It has great action sequences, interesting characters, and a story that was created specifically for the anime.