As I've mentioned before, I think the Godfather is a highly over-rated movie. I sat through the first one wondering why I should care about any of these characters. I can only guess that the people who review it positively have a completely different cultural view-point from me. I don't understand the praise or the interest. Mob movies generally do very little for me. A clever criminal movie might work, but two families of mobsters, not so much.
Then again, I do not enjoy watching TV shows that seem to bask in bathing in human sewage and claiming to be drama. But these very shows seem to be incredibly popular: Game of Thrones, US version of House of Cards, The Wire, Breaking Bad, and The Borges are perfect examples. Someone watches these, but they don't interest me at all. (US House of Cards is a mild curiosity, but just to see how they handle the story differently from the original UK version, but US version is distinctly inferior in every respect)
Other movies are considered cultural icons, but I think they're pretty over-rated. The Graduate and 2001:A Space Odyssey both spring to mind. Sure, they might have been interesting at the time, but were they all that good? meh.