In some ways, they're not creatures at all, but rather characters just like Harry, Ron, Dumbledore, and all the other living people in the books.
Ghosts can pass through solid objects.
They do not eat, but in many other ways they seem to enjoy a full life. There are differences, however. They don't all get along exactly well, either. The Ministry of Magic has some authority over ghostly behavior. JKR has suggested that we will learn the answer to this in upcoming books.