I watched The Godfather for the first time when I was 13 or so. I enjoyed certain parts of it, but the overall point of the movie - the character development, the themes of family and responsibility, crime vs. respect and if they can coexist, etc. - were totally lost on me. It was long, and I probably didn't pay enough attention. I saw it again as a freshman in college. I "got it," loved it, and have watched it several times since. I own the trilogy on DVD and have also enjoyed the second film several times, but I've never even bothered to watch the third because, even though I know it is a decent movie, I would rather think of the Godfather as parts one and two only.
P.S. I think the first is a little better than the second, even though the second is amazing. Why? Marlon Brando. And it's a little shorter and more entertaining, quotable, etc.