I always hesitate before I vote on this particular question. While I definitely agree, the first is the original, a classic, a perfect masterpiece, I can't help but be drawn to GFII, so that's what I voted for.
I guess, for me anyway, I loved the flashback scenes and the early days of Vito. I liked the to see the characters evolve; the way Michael became a cold hearted killer; Kay finally having enough and getting an abortion (unheard of and unacceptable at that time); Connie going from shy/timid punching bag, to leaving her kids and traveling the world with strange men...and poor Fredo being booted from the family (and later killed) by his little brother.

Heck, the first two are both "great", but I had to pick one, so I went with GFII.
As far as GFIII goes, it's the least likeable of the three, but on it's own it isn't a bad movie, no match for the first two, but not a bad movie. I found the whole Vatican storyline confusing and a little boring. I didn't like the Vincent character popping up...I do agree that the ending scene was powerful, and as usual Pacino was his usual best.
TIS