This is an interesting subject because many people will say different things. Some will say 'The Godfather' trilogy (although I wouldn't because I absolutely hated part III and would never soil the good name of the first two by associating them with it). Some may also say the Dollars trilogy, but I can't call it a trilogy if the films don't have recurring characters and the stories don't play into one another.
For me, I'm going to have to go with the original 'Star Wars' trilogy. Each film played off the previous perfectly and I still find time to watch them each at least once a year.
I'd like to also throw out an oft unmentioned trilogy which I, as a science fiction fan, have enjoyed immensely over the years and that is the Star Trek trilogy going from Part II 'The Wrath of Khan', through part III 'The Search For Spock', and finally part IV 'The Voyage Home'. They are each great films in their own right, but all three together play out one whole story from beginning to end that is pretty damn entertaining and represents, in my opinion, the best of what the Trek films (now 12 of them) have to offer.
For me, I'm going to have to go with the original 'Star Wars' trilogy. Each film played off the previous perfectly and I still find time to watch them each at least once a year.
I'd like to also throw out an oft unmentioned trilogy which I, as a science fiction fan, have enjoyed immensely over the years and that is the Star Trek trilogy going from Part II 'The Wrath of Khan', through part III 'The Search For Spock', and finally part IV 'The Voyage Home'. They are each great films in their own right, but all three together play out one whole story from beginning to end that is pretty damn entertaining and represents, in my opinion, the best of what the Trek films (now 12 of them) have to offer.