Cowboy Bebop is something of an essence of a future dystopia.
Mankind has conquerored the stars. We've got homes on moons of Jupiter, a dome on Mars, a prison outpost on Pluto, and the Earth is largely abandoned. What made this possible was a system of "gates," basically portals between distant locations in space-time.
But what has it brought us? Wars were faught on desert moons. Mars is corrupted with drugs and organized crime. The gates are targets for terrorists. Where the night sky was filled with stars once, it is now cluttered with floating ads to catch the attention of those in space, hoping to give them the next fix with bright and shiny letters, when they are seeking what their life is missing.
Enter four characters who are missing something in their life. Jet Black, former cop, whose mechanical arm is a constant reminder of a deep betrayal. He took up a life of bounty hunting afterwards, to find some direction late in his life. He met Spike Spiegel, a smooth-talking ex-syndicate member who is missing the only part of his soul that made him feel alive (he's pretty much the main character, but they tell everyone's story). Together they traveled the universe, hunting bounty heads for paltry sums, each directionless, wandering.
Enter Faye Valentine, a woman without a past whose present is a mounting debt and a knack for 'womanly wiles'. Enter "Radical Edward," a hacker child without a family, who forces her way onto the Bebop (Jet's ship), and proves somewhat useful.
As the series progresses, they pick up Faye, Ed, and a hyper-intelligent pooch, have a few adventures, discover a bit about their pasts, and then loose them, telling the story of four people missing something deep, who managed to find it amongst the stars, and the glittering ads.
The series oozes style, complete with music by Yokko Kanno that jumps genres and is often set to emotionally charged scenes in unique ways. Directed by Shinricho Wantanabe (he's done some other fantastic stuff), it captures a lost society, four people lost within it, and how finding yourself in life is something of a constant, even if you fly badass spaceships or travel between Mars and Callisto in an interstellar gateway.
More specifically, it's four characters who are always poor, and who hunt bounties to make ends meet, and their trials and travails. It's the perfect D&D setup -- Four characters in space, with a motive to hunt down targets, have adenture capturing them (without killing them), and live day to day.