It wasn't my favorite, but it certainly made the deepest impression on me when I was about 5 years old:
"The Little Match Girl", by Hans Christian Andersen
I cried and cried over the little girl's fate when my mom read the story to me. She was only able to console me by assuring me that it was only a story, and that it didn't really happen.
http://www.digregor.com/FairyTales/matchgirl.html