Your three movies you either watch over and over or have changed your life since you saw them. They don't need to be connected in any way. Mine: A Clockwork Orange Nil By Mouth Trainspotting
Isn't Trilogy a set of films that tells a three part tale, like The Godfather saga, Star Wars (first trilogy...the one that counts), LOTR? Maybe you should have titled the thread "Favorite Trio of Films"? In that case, my most watched trio are: Enter The Dragon - I stopped counting how many times I have watched this movie many years ago when it reached like the 90th viewing, but I watch it at least yearly during the last decade. King Kong (1933) - Kong have been part of my life since I was a preschooler. I know every frame of that film. If a clip of it shows up on tv, I stop everything I do it and watch it. Star Wars (1977) - I hate to call it "A New Hope" since that was added years after its original release. This is my second most watched film of all time. When I watched it for the first time back in the summer of 1977 in a jam packed movie theater (fire department could have given a hefty citation since they have people seating on the aisles since all seats were taken), it blew me away like no other film before or since. I, and the audience, got completely immersed in that viewing experience and remains the most fun I ever had at a movie theater.
In answer to your question, yes. But the term "holy trilogy" is usually used as a term for three top anything in their field or for an era. Three top basketball players. Three top bands, etc. What I meant was three films that are the most personal to you. Plus, as you can see by the spelling, I was drunker than shit when I started this thread.