I've cheated ever so slightly on this one for the simple reason that it is so long since I read any of these books, that I actually can't remember much detail about any of them. Only one of them (The Woodcutter) is strictly about fairytales, but the others are still reimagined children's tales, so I'm going to count them!
One thing that all three books have in common is that they are much much darker than their origin stories. The Woodcutter is set in a fairytale world more akin to the original Grimm fairytales than their Disney counterparts and it is the woodcutter himself (usually relegated to a side character) who is the hero of the story - he is the one who must ensure that justice is served and everything is as it should be.
Wicked is the story of the witches of Oz and presents a much more humanised version of the Wicked Witch of the West than the one we are accustomed to. Other characters, both major and minor, are given far darker significance and Dorothy - the lead in the original story - is barely mentioned at all. It didn't make me see the original book or the film in a different light, but rather, seemed more like a separate story entirely. Although I enjoyed it, I didn't want to read the rest of the series, as it was too dark for my tastes. On a side note - if you have seen the musical and want to read the book it was based on, do so with caution - the book and the musical are VERY different.
The Looking Glass Wars is probably my favourite of these three books and is based on the story of Alice's Adventures in Wonderland. It is based on the premise that the Alice from Wonderland is a real person and that Wonderland is real. Alice ends up in the human world and gradually becomes convinced that Wonderland was all in her imagination. However, she is now the true ruler and her people want her back in place of her Aunt Redd who stole the throne from the White Queen, Alice's mother. It is a wonderfully bizarre piece of fiction and despite its fantasy style, is a 'believable' explanation of the original story.
Much as I like the theory behind this kind of book, it's something I haven't read a huge amount of, but these are three excellent examples of the genre.