Time to type.
Contrary to my belief no one's listed the Apes trilogy yet. I thought for sure 1SO would. Didn't he say something about it being the best current action franchise last year?I didn't even consider the Apes trilogy and I think that's because I'm still feeling burned by the severe change of tone away from action adventure in the 3rd film. Much like back when Mad Max was a proper trilogy there were two great films followed by Thunderdome, which had the look and feel of Mad Max, but the story went to a place I never wanted Max to go, giving hope and saving children. It tainted the entire trilogy for me even though I wouldn't say Thunderdome is a bad film. It's just too radically different.
Series that do not meet my definition of trilogy: Alien, Mad Max, MCU movies, MI, Rocky, Terminator, James Bond, other thingsI asked a friend at work for his favorite and his answer tickled me. "The Fast & Furious trilogy that contains both Paul Walker and The Rock."
Your exclusions are interesting because by your very reasons for excluding them...
Star Wars is a series of what will be 9 films. So calling your favorite the "Original" trilogy is the same as saying Rocky I - III or the first 3 Alien films.
Lord of the Rings stopped being a trilogy once Peter Jackson unleashed The Hobbit. It is now part of a series.
The Dark Knight trilogy are just 3 Batman movies from a large and ongoing franchise. By your own definition, not a trilogy.
The Apes... well you can see where I'm going. The 3 latest films even make sure to connect to the previous Blockbuster franchise. I can see excluding the Tim Burton film, but the other 8 films bust the definition of trilogy.
Let's start with the big one. Star Wars
is technically more than just three movies but it really is a series of disconnected trilogies. Each trilogy is a self contained story that you can watch independently of the other ones. The individual movies are both books in a long series and chapters of a three part story. George Lucas always conceived SW in this way: three large stories, told through three movies each, both separate and connected.
Choosing one trilogy is not arbitrary. Picking episodes 6 through 8 as a trilogy for this Top 5 would be, which to me is the equivalent of what you're doing with, say, Rocky. The Rocky movies were not written with an intended three movie arc for the first three. Their plots are all self contained and there is no more connection between any successive three episodes than the others - is my understanding, I haven't actually watched them. Episode 6 concludes a trilogy, Rocky 3 just solves the plot of Rocky 3.
The Hobbit being a prelude to LOTR does not mean the two stories are not separate. They are two independent quests, connected by many elements but self-contained. Being part of the same world does not mean they tell the same story. One is about kicking Smaug's ass and the other is about Middle Earth return policy for jewellery. Would you include a Silmarillion movie in the LOTR series if it dealt with Sauron?
Not just that, but both trilogies are separated by their tones. The Hobbit is a mess tonally but it often tries for a fable feel and is generally more lighthearted than LOTR. The latter is darker and quickly adopts and epic scale where TH is generally a more intimate story. It's difficult to make generalisations about TH because that thing is all over the place.
The Dark Knight is not in the same series as the other Batman movies. Whether you believe in continuity for the others or not, Batman Begins reboots the series. It is as connected to the Burton et all. stuff as The Amazing Spider-Man is to the Sam Raimi movies - or Homecoming for that matter. Not just that, but Nolan created his trilogy to be a full arc that would tell a unified story of Batman, from his Inception to his death. Ledger dying sort of ruined his original plans, but the trilogy is its own thing - a self-contained story, unity of talent, creative and thespian, a particular tone that was new at the time, etc.
If you consider all the Batman movies to be part of the same series I don't see how Apes can possibly not be a trilogy. Maybe War is a bit different in what it does, but surely that difference is microscopic compared to the Pacific-wide distance between TDK and George Clooney's nipples?