Godfather is THE trilogy... to me, when someone says trilogy, that is what comes to mind.
Other honorable mentions:
-Star Wars 4-6
-This is technically not a trilogy, but Star Trek 2, 3 & 4 are a continuous story and are truly the shining light of the franchise that has been ruined by terrible plots (Nemesis) and actors thinking they are A-List (Brent Spiner, and to a lesser extent Patrick Stewart)
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