The one and only film I will never get tired of watching is Fight Club. It is my all time favorite film. I once watched Fight Club thrice in a row! I can really relate to the movie and it brings out so many emotions. I would pick Fight Club over any new or old films you offer me. PS. For those who haven't watched it yet, try it. You won't regret it.
For me it has to be either the Lord of the Rings series or Fight Club. I saw Lord of the Rings for the first time when I was around 10 years old and I still watch it at least twice a year. But in the last few years I watched Fight Club a lot because every time I watch it I realize something new about the movie.
I can watch most of the Disney movies over and over without ever getting tired. They bring nostalgia and I can sing to all of them. There are a few I wouldn't want to watch a million times like Dumbo or Pinocchio, but other than that, bring it on. Phantom Of The Opera I can watch a million times as well, it doesn't matter which one. I love that play/book/movie. It is so amazing.
When I was younger I remember watching "Speed" over and over again. Then when I got older I found "The Naked Gun" series and honestly I could watch those or any Mel Brooks film over and over again without any issue. There's something about them that just makes me laugh even if I've seen a gag multiple times.
There are a lot of movies I never get tired of seeing. I never get tired of seeing Clue, A Christmas Story, 12 Angry Men, Psycho, Rear Window, as well as many others. I can watch all of them over and over and never get tired of them. Some of them I watched so much I can recite some of the dialogue.