The future has been a discussion in science fiction for decades. Anime is not an exception to this, as anime about humanity's future has been produced for years. Alternative Future Animes have become a niche I usually think of three whenever I recommend an alternative future anime to a friend.
1.) Neon Genesis Evangelion
This anime has been revered by a large portion of the anime community as a classic. For those who haven't seen it, Neon Genesis Evangelion is an anime about a post apocalyptic future, where the earth is constantly attacked by giant monsters called Angels (sweet, sweet irony). The earth's only salvation are a couple teenagers and giant bio-machines which they pilot. The story took place 25 years ahead of when it was published, now 2015. The main character, Shinji Ikari, does get annoying; but the fight scenes and character development... of everyone else, makes it worth watching.
2.) Cowboy Bebop
Cowboy Bebop is considered as an anime 'you need to watch before you die' by the entire anime community, and for good reason. Cowboy Bebop tells the tale of a bounty hunter on the ship known as the Bebop, in 2093. It shows how the future progressed into the stars, moving onto the different planets in our solar system and showing the new ways of crime. The characters are brilliant, especially the main character, Spike Spiegel. This show elaborates on how the 'long-term future of the human race must be in space', and how humanity will progress into it.
What if there was a way that society could predict who would commit crime? Psycho-Pass answers this question, with a future controlled by the Sybil system. This system gives every human being a number: the higher the number, the more likely you are to commit crime. Of course, the best way to smoke out criminals is with other criminals. That's where the Public Safety Bureau comes in, with both investigators and enforcers. The characters of the show have great backstories and motivation, and it has inspired live action movies to be made.
Futuristic anime have become more and more popular as time goes on, being as the genre leaves the rules entirely up to the creator. The future, either dystopian or not, is full of possibilities. It's only up to us to see what lies ahead.