I didn't see Godfather until about four years ago, and still haven't seen Part 2. But yeah, it's one of those things whose influence has reverberated through pretty much everything since.
(Matt Groening once joked that the first time Simpsons fans saw Citizen Kane they'd be surprised, since Simpsons has homaged pretty much every scene in the movie at one time or another. Godfather is that kind of movie -- it's a defining classic that influences everything that comes after, either in subtle stylistic and thematic ways or through full-blown parody.)
And sometimes stuff like that is so revered that, when people finally get around to checking out the original, they don't understand what the big deal is. Godfather is not one of those movies, at least not for me -- and neither are greats like Citizen Kane or Casablanca. I watched them and I knew why they were such towering classics.