The Ghost and Mrs. Muir is one of my favorite films. It is a ghost story/romance starring Rex Harrison as the ghost of the sea captain, Gene Tierney as the young widow Lucy Muir who rents the cottage by the sea, Natalie Wood as Mrs. Muir's daughter and Edna Best as the housekeeper. George Sanders plays Lucy's suitor. The movie is directed by Joseph Mankiewicz, who also directed Julius Caesar, Guys and Dolls and Sleuth.
Youtube has the entire film divided up into sections, which should autoplay from here:
There was a short-lived tv series based on the film.
1/15/2008: 1001Flicks has a review.
7/14/2008: Another Old Movie Blog's review has lots of spoilers.