Ride Back

Watch: http://www.animeshippuuden.com/category/ride-back/
12 episodes

Read about it: http://en.wikipedia.org/wiki/Rideback

Manga: http://www.mangafox.com/manga/ride_back/
Its ongoing. Ride now there are only chapters 1 and 1.5

You're not going to find ANY romance here.
I loved it anyway. Great anime.

The ending was very emotional.
Not because it was sad but it was so heart warming.

Earlier in the series at a protest, one of Rin's friends chases the train that Rin is on.
She's yelling for Rin to dance again when she is killed.

Rin battles with Fuego (her ride back) and it looks like she is dancing.
Fuego can barely keep up with her and eventually its destroyed.

You'll see Rin pick up her ballet shoes in the final episode.