Most of my books have retained the same cover as they moved from hardcover to paperback. Two– The Masque of the Black Tulip and The Betrayal of the Blood Lily— have undergone dramatic transformations.
For fun, here are the before and after pictures:
The Masque of the Black Tulip (2005, 2006):
The Betrayal of the Blood Lily (2010, 2011):
I have to admit, I rather like having two different images for hardcover and paperback. Do you prefer different covers for different formats, or the same cover for both?