Just adding my two cents to the great reviews already here!
I saw this series when it was broadcast on Cartoon Network a few years ago, and I was hooked on it from the first episode! I'm not usually a fan of big robots that duke it out in the streets, but the characters and the visual style of this anime really drew me in. I'm a big fan of Art Deco (same reason I liked Batman: The Animated Series, which shares some of the same production staff), and this series is loaded with it, from the buildings, to the vehicles, to the film noir feeling that pervades the entire series.
Roger Smith is probably one of the smoothest cats in anime, yet even he gets blindsided every now and then by questions from his unflappable robot maid/ward/royal pain in the keister, R. Dorothy Wayneright.
Case in point: Roger and Dorothy are investigating the kidnapping of the son of a prominent Paradigm industrialist (in the episode, "Beck Comes Back"). Discussing the son's parents, who met after losing their memories in the Event, Dorothy says she has two questions for Roger. The first one is, "Does losing your memory really make you that lonely?" Roger says it's a tough question to answer, but makes a go of it, then asks Dorothy what the 2nd question is. "Forget it," she says. "If you thought the last one was tough, this one is worse." Dorothy is damaged in the battle to retrieve the industrialist's son, and Roger asks Norman, his capable butler, to take care in repairing her so she can ask the question...and what is the question? "If you and I lost our memories, and we met, would we fall in love?" That one renders Roger speechless...
There are many such moments, as well as ones that speak a little too close to home, such as the dangers of genetic manipulation, nuclear holocaust, and evil that disguises itself as benevolence.
Luckily there is a second set of 13 episodes to help answer some of the questions raised by the first season! The voice acting is well done (you'll hear familiar voices if you're a fan of Cowboy Bebop) and the music is very cool. Enjoy!