To me the film is still fresh and interesting, even though I've seen parts of it at least 100 times -- to the point where I've got a lot of the dialog memorized. My wife doesn't share the fascination, but my sons do. It's a guy thing, I suppose.
The genre of gangster films, however, doesn't interest me. It's this specific film. Nor am I equally captivated by the Godfather sequels. What is it about The Godfather that's so great? Just about everything: the character definition, the plot, the scenery and sets, the casting, the music, the dialog, the acting, the photography...
Although the film is on everyone's top-five list, it isn't perfect. IMDB shows about 100 goofs. Even finding the goofs, however, has become a sport.
Financially, The Godfather has generated over $250 million in revenue against a $6 million production budget. It saved Paramount Pictures, and it propelled the careers of names you know (e.g. Diane Keaton) and names you might not (e.g. Peter Bart). Culturally it opened a decade of blockbuster films (e.g. Jaws) and repositioned the entire film industry after a very trying 25 years -- the end of the studio system, the advent of television, and the demise of the Motion Picture Production Code.
A magnificent achievement, and one I hope to enjoy for years to come.
