Fleshy Head

Mummified Edmontosaurus regalis (a herbivorous duck-billed dinosaur that is a member of the hadrosaurid family that lived between 75 and 65 million years ago) remains have been found in Alberta, Canada, with it's fleshy head ornament completely preserved. This is the first evidence of a dinosaur having a completely soft tissue crest - up to now, only bony crests have been preserved, as skin rarely fossilises. When the dinosaur died, it would have been buried instantly in sediments, where there would have been a lack of oxygen, slowing down the process of decay and allowing soft tissue to be mineralised.
The paper published in Current Biology (which unfortunately I can't get full access to without paying $30!) explains that the fleshy head ornament would have replaced the bony crests in hadrosaurids at the end of the Cretaceous (around 66 million years ago). It would have been used in a visual display to attract mates or to determine leadership in a herd.

A reconstruction of the fleshy head (courtesy of the BBC)

Other dinosaurs have been previously found with some soft tissue preservation. An article in Nature explains how a 113 million year old Scipionyx samniticus (a therapod dinosaur) fossil has been found with soft tissue preservation, whilst National Geographic explains about how a 70 million year old Tyrannosaurus rex fossil has also been found with some soft tissue from the thighbone.