This is it: the best trilogies I've seen... The best things that come in threes! Why? Because I love movies and yet my most viewed list is the "Movie Fails" list. This positive list is more how I feel about movies (although it is honestly more fun to trash the really bad ones).
If they made a fourth movie or beyond, I ignored those extra sequels and only counted the first three (for example: Indiana Jones IV). If I haven't seen all three, I couldn't really list them (so my apologies to fans of The Jetsons trilogy).
Although I considered my total ratings for all the parts of a trilogy, I still ranked these in order based on overall impression of the whole trilogy. For example Star Wars totalled 26/30 based on my own scores, but BRD trilogy was 28/30. Yet I ranked Star Wars higher because of its continuity from film to film, even though the individual BRD films were better as stand-alone features, in my opinion.
Brief explanations about my choices are included...
From the dark humor of Mr. Vengeance, to the violent grittiness of Oldboy, to the ultra-stylish look of Lady Vengeance, this trilogy has a lot of variety. The movies are all consistent in quality, and despite Oldboy being the most popular, you can make a solid argument for any one of them being the best of the three.
Three Colors Trilogy
The Polish Krzysztof Kieslowski made this trilogy to honor his adopted country, France. Amazingly the films are not only a reflection of the French identity - as the titles corresponding to the French flag suggests - but also a dissection of humanity itself. This trilogy was visually stunning, but I was even more impressed how so many themes tied together in each individual movie, as well as the trilogy as a whole. A must see.
The Apu Trilogy
Satyajit Ray's trilogy about Apu's life is a monster achievement in film. The brilliantly executed neo-realist style allows the viewer to be transported to India and be a part of a culture and lifestyle that many of us would never know.
Dark Knight Trilogy
The Dark Knight
The Dark Knight Rises
Financially and artistically this trilogy is a colossus! Chris Nolan gave us a minimal CGI, non-digital, realistic Batman. Realistic in the sense that there are no actual super powers or radioactive spiders, like the typical comic book movie. However the 3 films are still set in a surreal, neo-noir, movie world. Much like the ideas Nolan examined in Inception, Gotham City is like a dream version of New York City, and the characters are metaphors for our beliefs about good vs evil, and order vs chaos. This is one of the rare film trilogies that actually got better with each part.
Star Wars (Original Trilogy)
A New Hope
The Empire Strikes Back
Return of the Jedi
The pure fun of A New Hope and the brilliance of The Empire Strikes Back, more than make up for the embarrassing sellout nature of Return of the Jedi.
The Marriage of Maria Braun
Fassbinder's examination of three different women in postwar Germany is a solid collection of films. The stories are interesting, the acting is solid and the directing is some of Fassbinder's finest work.
Lord of the Rings
LOTR: The Fellowship of the Ring
The Two Towers
Return of the King
Despite the fanboy worship, LOTR is not perfect cinema, and I believe there is enough room for The Hobbit(s) to possibly surpass these films. The slower moving extended versions are slightly better than the theatrical ones. As an adaptation of a popular book series, Peter Jackson was efficient in what he chose to film and yet respectful of the source material. Quite a remarkable achievement considering the countless films have had such mixed results in attempting a similar task.
Mad Max Trilogy
The Road Warrior
Mad Max: Beyond Thunderdome
The grandfather of the post-apocalyptic action movie! This trilogy combines tried and true car chase scenes with the bleakest dystopian sci-fi themes. Great stunt work and simple survival plotlines make these films accessible as well as timeless. Yet again we see a third movie that was an attempt to please a wider audience, and yet again it is the weakest of the three. In this case the Ewoks are feral children.
Man with no Name
A Fistful of Dollars
A Few Dollars More
The Good, the Bad, and the Ugly.
Fistful of Dollars is less exciting than Yojimbo but still an interesting interpretation. The second film is just an average, forgettable western. The third film in the trilogy is widely viewed as a classic of the Western Genre.
This trilogy is famous for its genre jump from horror to action. Then along came the much hated Alien 3. As much as the third part worked as a decent low budget suspense film, the original production was supposed to be a massive epic about the Aliens finally invading a futuristic earth! Too bad, the franchise just continued downhill from there...