Cowboy Bebop is an anime series that can pretty much be categorized as its own genre as while it predominately remains a sci fi western, it also contains elements from film noir to blaxploitation that gives it a style that's all it own. Cowboy Bebop is mostly a episodic series that follows a crew of bounty hunters that are ultimately trying to reconcile their pasts and at the end of the day, hopefully put food on the table. Cowboy Bebop features some animation that is about as fluid as water, some incredibly memorable characters with some great chemistry and characterization and a jazzy soundtrack composed by Yoko Kanno, who is arguably one of the greatest composers in the medium. I certainty consider Cowboy Bebop a classic and I strongly recommend seeing it if you haven't already as I think it's an series any anime fan should experience at least once.
Samurai Champloo is an action series that follows three characters on a journey to find a samurai who smells of sunflowers and it takes elements of a traditional samurai story and combines them with hip hop music which is evident in two of the main characters and their respective fighting styles. When it comes to anime and the action genre, Samurai Champloo has some the best fight chereography you can find and its soundtrack, produced by Nujabes suits the series incredibly well with its blend of traditional beats and Japanese influence.
Shinsekai Yori is a sci fi fantasy that takes place in a dystopian utopia set over a thousand years in the future and focuses on a group of children learning to use their psychic powers and dealing with the consequences of learning about their society's history. Shinsekai Yori features some great world building, a consistently dark atmosphere and some very mature themes and topics such as sexuality and the human condition. SSY is a series that I would not consider a easily digestible, it will force you to think and hopefully reward you in doing so. If that interests you at all, then please by all means give it a watch.