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Here's a list of trilogies:

American Pie
Austin Powers
Back to the Future
The Bad News Bears
Beverly Hills Cop
Crocodile Dundee
The Crow
Die Hard
The Exorcist
Free Willy
Friday
The Godfather
Indiana Jones
Jurassic Park
The Lord of the Rings
Mad Max
Mad Max
The Matrix
The Mighty Ducks
Missing in Action
The Naked Gun
The Omen
Poison Ivy
Poltergeist
Porky's
Psycho
Rambo
Robocop
Scary Movie
Scream
Shaft
Sometimes They Come Back
Spy Kids
Star Wars (x2)
The Terminator
Kevin Smith's New Jersey trilogy (Clerks, Mallrats, and Chasing Amy)
Krzysztof Kieslowski's Three Colors trilogy: , , and
Baz Luhrmann's red curtain trilogy
Robert Rodriguez's El Mariachi trilogy
The Hannibal Lecter trilogy
Sergio Leone's spaghetti western trilogy
Godfrey Reggio's Qatsi trilogy

There were 4 Alien movies, but I really don't think Sigourney could have sunk this far.