Despite what the title of this post says, I actually love the story of Cinderella. It's been my favorite since I was a little girl. I love the way the story flows and I used to wish it would happen to me.
But let's look seriously at how realistic this story is (ignoring the fairy godmother part, because I like a little magic in my stories).
A girl is doing something innocent, like shopping with her family (her step-sisters and step-mother, who are naturally evil, are making her carry everything). She nearly gets run down by a carriage, which came out of no where and disappeared back into no where just as quickly, and a prince who is hiding who he is comes to help her gather her things back up. This is, of course, the boy mets girl section of the story. It's nice, they feel something for each other, but aren't sure what. And as quickly as they meet, they are pulled apart, back into their normal worlds.
Girl goes home to cook, clean, and do all the household chores while her family gets to rest and yet she's still prettier than they are.
Boy goes back to the palace and finds that his parents are throwing a party to find him a wife. Every eligible girl will be there to throw themselves at him because, well, he's the prince.
Girl magically gets to the party, looking prettier than anyone else. She is unrecognized by her family, or even the prince (who can be forgiven, because they only had a brief meeting). They fall in love at first, well technically second, sight (I'm not saying this is impossible, it's just very improbable). They spend the entire time she has available at the ball together, until she dashes off at midnight, leaving behind a glass slipper (which is a silly shoe type for dancing or even walking, in my opinion).
Boy travels throughout the kingdom trying glass slipper on everyone's foot, trying to find his girl (ignoring body type, rough height, and facial characteristics to rule out most of the people he's coming in contact with. This part works better if it's only a servant sent out, since he probably wouldn't know such things).
Evil step-mother locks girl away to keep her from getting to try on the slipper, because she's figured out who they are searching for. She's hoping one of her daughters will mysteriously have the exact same shoe size, even though she should know what shoe sizes everyone has (at least roughly, because don't most girls borrow each others shoes?).
Despite step-mother's attempts, girl ends up running into prince/servant. She tries on the glass slipper (or produces it's match) and reveals to everyone that she was the one who the prince fell in love with. She's swept off to marry him, almost immediately.
It's all, I guess, possible, it's just extremely unlikely. Mostly that a father who loves his daughter, like Cinderella's father obviously did, would leave her in the care of someone like her step-mother could only possibly happen if he died shortly after the wedding (within days, possibly).
And why are the prince's parents so interested in him getting married so quickly. They aren't likely to be dying anytime soon, so it seems odd that they are want him to produce an heir already. And don't princes normally get married for political reasons?
The story is great, I love it, but when you shine the light of reality on it, it becomes obvious that it's just a story and unlikely to happen in real life. Impossible when you add the fairy godmother into the mix (she's a wonderful dues ex machina to move the story along and get Cinderella to the ball).
And yet, I love the idea of the impossible happening, which probably explains why I love this story so much even when I look at it knowing these things are impossible.