I left out films such as Indiana Jones, Die Hard, Bourne, Alien, etc. since they're no longer trilogies, also omitted Avengers because it's getting a fourth film.
Anyways, of the choices given, I'd have to say the Lord of the Rings trilogy, all 3 movies were absolutely mind-blowing. It's also one of the few trilogies that gets better, and not worse with each installment. It pains me to say the Matrix trilogy doesn't pass the muster test (speaking strictly for myself) despite the original being my favorite movie with the shitty third film and the disappointing second movie.
It was a tough call between LotR and the original Star Wars trilogy, I ultimately went with LotR just because of the quality of the third film in each series. While Return of the King eclipses the other 2 films, Return of the Jedi was a step back from the first 2 original Star Wars movies in terms of quality, so I voted Lord of the Rings just based on consistency.