Two of the best-known stories that went from great short story to brilliant novel are Isaac Asimov's Nightfall and Orson Scott Card's Ender's Game. Both were excellent stories in each instance.
The fascination comes in being able to see how the short story brings out the situation quickly, then resolves it, while the novel brings out the details, information and characters that bring the surrounding story to life.
Take Ender's Game, for example. The short story is about a young boy who goes to Battle School, and saves the world from alien invasion without knowing it. The novel gets into how he gets into Battle School, more of his training, and what his family is doing. Much more depth, and not only did this make sequels possible, it allowed for more novels focused on one of the other children from Battle School. All well done.
It's similar for Nightfall. A world with five suns that has never known night... except once every couple thousand years. The inhabitants don't believe in night, save for a few religious crackpots, but scientists are discovering evidence that something indeed happens. The novel goes into further detail as to the discoveries as well as the aftermath, when much of the world has gone insane from the unfamiliar darkness.
But I also enjoy finding stories that aren't so well known. Eric Frank Russell's Plus X and variants thereof, for example. This is an interesting case because I like the shortest version best. EFR's strength was definitely in shorter stories. His works are hard to find, appearing rarely in bookstores, but what booklover minds an excuse to haunt the local used bookstore?
I like best finding books that were made into movies, not movies made into books. It's just interesting seeing where the movie had to make changes to how things went in the book, while a book can stay more true to a movie.
Dune is a prime example. The novel is great. The movie... depends on which one you like best. Some prefer David Lynch's version, others the miniseries that aired on the Sci-Fi Channel. You can read reviews on each and get extremely different opinions.
I love it when I discover a new way to experience a story I've enjoyed, whether it be an older version or newer. There's just something about it.