I've always believed that the overriding message of the GF Trilogy is: crime doesn't pay. Michael--brilliant tactician, numero-uno gangster, global crime bigshot--lost his family and died alone, attended only by a little dog. His losses are reinforced by his primeval scream when his beloved daughter dies, and while (as that moving Intermezzo Sinfonico from "Cavalleria Rusticana" plays hauntingly) his memories of happy times with Appolonia and Kay swirl around. It's telling us: look how this supposedly all-powerful pezzanovane ended up.
Crime didn't pay for Vito, either. True, he dies in his tomato garden, playing with his grandson. But that earlier, touching scene with Michael shows him exhausted by life after losing his eldest son and having his youngest, on whom he'd pinned such high hopes, forced into a life of crime.