I finally got the DVD set from Amazon and I can understand what the fuss is all about.
This anime' series is highly regarded in the fan community for it's attempt to get all the technology and science "right". It is set in the near future and almost all the action happens in low Eath orbit. No Interplanetary stuff, no aliens, everything grounded in realism.
The story revolves around a motley crew of unloved and under-funded second-stringers who's job is to track down and dispose of space junk that's become a hazard to navigation, a vital job that nevertheless has the lowest status of all. Over the series most of the character's motivations and backgrounds are explored. The rest is classic boy-meets-girl, though in an unusual context - but I found the plot lines refreshing, and it played out like a well-thought-out novel, with geo-spacial politics and corporate intrigue trading equal time with star-crossed romance. By turns amusing, romantic, and thoughtful, this might make a good series to watch with your significant other as a way to break them into good anime'.
The first episode is the weakest, so if you don't like it I encourage you to stick with it for the first three episodes, and I think you'll be hooked. I thought the ending episode a little rushed, but satisfying, after having learned enough about the characters to care a bit about their outcomes.
The English voice dubbing is a little uneven regarding the emotion levels, so if you don't mind subtitles, I would suggest watching it that way.
This is a little taste of the show from a Bandai promo.
The opening title montage for the series. If this reminds you of the opening credits for Star Trek: Enterprise, good eye.