It's 2020 in Japan and post-world war three. The left over technology from the war is finding its way into civilian hands, the Rideback transformable motorcycle is one of those devices.
Rin, the main character, is a former ballet dancer who is one of the only people able to ride the machine without all the electronic supports in place. I'm only a couple of episodes in, but the story is very coherent for a Japanese animation (they aren't always). The main character is already well developed and they aren't shy about explaining the technology.
The story arc looks like it's headed for a large political showdown with a despotic government, but ingenues on transformable motorcycles are just what you need in those circumstances.
The animation (if you're into that sort of thing) is a modern mix of computer and cell and shows off some very complex physics as well as excellent detail.
If you like anime, you'll enjoy this series. If you like anime and motorbikes this one is a must see.
Some Rideback links:http://www.madman.com.au/series/home/16127/rideback
The Australian site (in English!)
The Japanese TV site
Rideback overview on wikipedia
Funimation, the North American anime company that brought Rideback in
You can do what I did and get it on Amazon. It's also available on itunes or through the Funimation site.