I am truly amazed how great this show turns out to be from a science-fiction fan's point of view, and I do not mean the kind of movie science fiction which relies on CGI as its main asset and suffers from poor unrealistic plot. I mean the kind of literary science fiction that gets awarded with a Hugo award.
Perhaps one should forget that this is an anime, for the simple reason that the stereotype of anime is something like a TV show for kids where a bunch of clichéd, depth-less characters battle supernatural enemies with their superpowers. If that is what anime means for you, think of Planetes as an animated series made in Japan. Removed around eighty years from the times it was made in, it presents quite a believable picture of what space exploration might be like at the end of the 21st century, with a load of detail comparable only to the movie adaptation of 2001: A Space Odyssey. This is one of the strongest points of the show - the richness of little details, like how rooms have to be adapted to zero G, makes the sci fi elements more believable.
The strongest point, however, would be how great science fiction this is. One definition of science fiction would be that a science fiction story depicts the way more-or-less imaginary technology (or the fruit of some science not directly related to technology, like chemistry) impacts human lives. Apart from the development of the regular characters of the show, every episode contains a story in that vein, with a great deal of insight and care for consistency. It is harder to show something gripping in science fiction with more-or-less realistic technology than in a flashy movie where the technology used is nothing short of magical, yet Planetes achieves that in every episode. Also, since the future gadgetry depicted is so often directly connected with the plot, and at the same time, so believable, Planetes could also be categorized as a cyberpunk show set in Earth's orbit, and I mean cyberpunk like in the later William Gibson stories, not like in, say, Cyber City Oedo 808. As I said, you won't see any technological magic, not even at the "AI virus gaining consciousness" level.
I'm sorry I can't recommend this further without any spoilers, but if you have ever enjoyed good SF literature, be sure to check out this show (at least the first 5 episodes, to see what it's like after we've gotten to know the main characters), and you won't be disappointed.