Trilogies:
American Pie Trilogy
Austin Powers Trilogy
Back to the Future Trilogy
Beverly Hills Cop Trilogy
Die Hard Trilogy
Indiana Jones Trilogy
Jurassic Park Trilogy
Lord of the Rings Extended Trilogy
Major League Trilogy
Naked Gun Trilogy
Rambo Trilogy
RoboCop Trilogy
Star Wars (original) Trilogy
Teenage Mutant Ninja Turtles Trilogy
Terminator Trilogy

Full Series (2 or more):
48 Hrs. (1 and 2)
Alien Quadrilogy
Analyze This/That
Bad Boys (1 and 2)
Batman (Batman, Batman Returns, Batman Forever, Batman and Robin)
Bill and Ted's Excellent Adventure/Bill and Ted's Bogus Journey
Bourne Identity/Bourne Supremacy
Chronicles of Riddick (Pitch Black and CoR)
City Slickers (1 and 2)
Conan the Barbarian/Conan the Destroyer
Death Wish series (own all 5, unfortunately)
Escape from New York/L.A.
Ghostbusters (1 and 2)
Gremlins (1 and 2)
Home Alone (1 and 2, - 3 and 4 don't count)
Fugitive/U.S. Marshals (technically not a series but the same characters)
Karate Kid series (1-4)
Lethal Weapon series
Monty Pythons movies (all but And Now For Something Completely Different)
Mummy series (Mummy and Mummy Returns)
Predator (1 and 2)
Rocky series (1-5)
Romancing the Stone/Jewel of the Nile
Rush Hour (1 and 2)
Shanghai Noon/Shanghai Knights
Spider-Man (1 and 2)
Superman (1-4)
Under Siege (1 and 2)
Wayne's World (1 and 2)
X-Men (1 and 2)

On my list/partially owned:
Blade Trilogy (own the first two)
Crocodile Dundee Trilogy (only own the first one)
Godfather Trilogy (own none)
Evil Dead Trilogy (own Army of Darkness)
Matrix Trilogy (own none)
Ring series (own the first)
Romero's Dead Series (own Night and Dawn)
Short Circuit (own the first)
Star Wars Prequel Trilogy (all but the 3rd obviously)
View Askes series (only own Clerks and Dogma)
Weekend at Bernie's (own the first)

Trilogy literally means a set of three literary works that develop a theme or subject. I would like to stick with trilogies, but yes, we can be liberal with it and include your collections/series that are two or more. It should be limited to movies however. Trilogies should be seperated so we can see them apart from the others and you can list your incomplete collections. My first post, or the way Linko listed are good examples.

Star Wars
Indiana Jones
Back To The Future
Lord of the Rings
Godfather
Austin Powers
Die Hard
Evil Dead
Matrix

Star Wars
Indiana Jones
Blade
Back to the Future
Trinity Collection (They call me Trinity, Trinity is Still my Name, Boot Hill)
Godfather
Terminator
Spy Kids
Spawn
The Mummy (The Mummy, Mummy Returns, Scorpion King)
Pink Panther
Hannibal (Silence of the Lambs, Hannibal, Red Dragon)
Man with no Name Trilogy
Matrix

Three Colors
Ultimate Matrix
Indiana Jones Trilogy
Star Wars Original Trilogy
Back to the Future Trilogy
The Samurai Trilogy (imo, best trilogy ever)
Godfather Trilogy
Man With No Name Trilogy
Lord of the Rings Trilogy

I'm a boxset sucker, so I have the complete runs of the following:

The Adventures of Antoine Doinel
Indiana Jones
Alien Quadrilogy
American Pie
Back to the Future
Die Hard (my first boxset & trilogy)
The Godfather
Harry Potter
The Jack Ryan DVD Collection
The Lord of the Rings Tilogy
The Lord of the Rings cartoons (The Hobbit, The Lord of the Rings, The Return of the King)
Man with No Name
Matrix
Robocop
Star Wars
Superman
Three Colors

Indiana Jones
Jurassic Park
LOTR:EE
SW trilogy
SW OT-dr. Gonzo LD-rips
Alien Quad

Trilogies
Star Wars
Indiana Jones
Back to the Future
Lord of the Rings
Terminator
Jersey Trilogy
Matrix
Jurassic Park
Harry Potter
American Pie
El Mariachi
Star Trek 2-4

3 or More
Superman
Alien

LOTR Extended Trilogy
Die Hard Trilogy
Alien QUADrilogy
Jurassic Park Trilogy
Superman QUADrilogy
Star Wars Original Trilogy

Looking to eventually complete:
Matrix
Blade

Just added Back to the Future Trilogy (thanks to the DDD sale!)

Indiana Jones
Jurassic Park
The Godfather trilogy
Star Wars