I think the original was the best, but that the 2nd film is usually regarded as most people's favorite on these boards. The second is more dynamic in its plot, especially with the two different story lines. But for me, the characters in the original are what sets it apart: Marlon Brando's portrayal of Vito, Sollozzo, Clemenza, Carlo, Sonny, Moe Green, and Tessio.
I like the third film if it were to stand on its own, but it has too much to live up to as a sequel and falls short because of a) Sophia Coppolla, b) the lack of Tom Hagen's character, and c) the lack of believability I have that Vincent could go from what he was at the beginning of III to the head of the Corleone's by the end.