I did some research to see if there exists an anime that was based on western stories and I have found some here (including the only one I can remember, Cinderella Monogatari). I have noticed that all anime there were old, thus, making me wonder if Japan totally stopped creating anime that are based on western stories.
No. There are a number of recent Japanese anime based on Western stories. Some examples:
- Gankutsuou: The Count of Monte Cristo based on Alexandre Dumas, père's classic French novel, Le Comte de Monte-Cristo, aired in 2004-5.
- Romeo × Juliet loosely based on William Shakespeare's classical play, Romeo and Juliet, along with numerous references and characters from other Shakespearean plays aired in 2007.
- Miyuki-chan in Wonderland is an erotic, lesbian rendition of Lewis Carroll's Alice's Adventures in Wonderland, aired in 1995.
- Powerpuff Girls Z is a magical girl anime series based on the American animated television series The Powerpuff Girls, aired in 2006-7.
- Deltora Quest based on the series of children's books of the same name, written by Australian author Emily Rodda, aired in 2007-8.
At least, there's the World Masterpiece Theater. Between 1969 and 1997, and 2007-2009, they produced anime based on a classic book or story, also western. I can't find anything that tells me whether it's over.
Besides from that, I don't know any anime based on western stories.