Cinderella is definitely a driving cultural force and such a household name that there is hair metal band from the 80s called Cinderella. She is constantly referenced in song, Disney made two sequels to their 1950s film and more. She's pretty much everywhere.
Also Cinderella III: A Twist in Time gets crazy.
I think the reason behind Cinderella's enduring popularity is to some extend, we all feel like Cinderella. Somebody is the Stepmother, keeping us down, whether it's The Man or ourselves or our bosses or significant others. Most people feel like they're just one great event from striking it rich, and everybody loves an underdog. Cinderella is an underdog who manages to get everything we think she wants, and it's all perfect and amazing. At some base level, it's what most of us wish we could have. (Note: Cinderella is collected in The Blue Fairy Book)