My first mind is to say Part II:
1) The ending scene with all of them at the table for Vito's birthday is still a favorite. What always strikes me in that scene is Fredo is the
only one to support Michael's decision to enlist. We also see Santino introducing his baby sister to the same man who he is going to have to lay hands on later and who will kill him in return.
2) Watching the story of how Vito came to America, built up what would become his family's legacy with his people in New York, and then get all the way back to Sicily and get revenge for his daddy, mama and brother was so sweet.
3) Watching Michael continue descending into the cold, ruthless man he was showing signs of being in Part I was fascinating, especially when it culminates in him having his own brother killed.
4) Seeing Michael interact with Tom Hagen and Fredo was always interesting; I always got the feeling they both might have been more intimidated by Michael than they ever were by Santino.
5) I think the best closing hit montage is still in Part I with Mo Green and the four families, followed by the Part III montage...but watching Rocco go on that suicide mission in the airport for Hyman Roth always makes me laugh.
6) Connie FINALLY coming off of that bullshyt when their mama died and coming on back home felt good...felt good to me, too, to watch her play Don (sort of) in Part III, though I know many people hate that installment of the story.
6) Lastly, a young Pacino and DeNiro in the same movie...very, very nice
Part I is always nice, though, because Santino is still alive, we get to see both civilian Michael and Don Michael Corleone and we get to go to Sicily and watch this man have a whole other life before he comes back home and starts another one lol.