The Lord of the Rings
The Dark Knight

Before I clicked on this I knew it had to be between Star Wars and Lord of the Rings.  It's a close call for me, but the Lord of the Rings had such a strong finish that it has to be #1.  My top 5 trilogies are:

1. Lord of the Rings
2. Star Wars
3. Captain America
4. Spider-Man 
5. Back to the Future


Honorable mention goes to the Dark Knight trilogy.  I also have to give a special mention to the X-Men prequels.  The first two movies were so good, that this trilogy could have easily ended up on my list.  Then Age of Apocalypse comes out and it's like a punch in the face.  The worst part is where they go to see Return of the Jedi in the movie and they say, "the third one is always the worst".  It's like they are mocking you while you watch their movie.

Lord of the Rings. Without question.
Those are my 3 favorite movies of all time.
I didn't watch them when they were in theaters when I was a little kid because I thought I was "too cool" to watch them. (We all know those kids and I'm sure most if not all of us have gone through that phase.)
Then, when I was in high school, I watched the Hobbit trilogy when those movies came out, and I remember really enjoying them. I did my research because I was interested in the world and the characters and I found out that it was a prequel to Lord of the Rings and thought, "Oh wow. Really?! Dang, I should actually sit down and watch those movie."
Then, I finally did and by the end of Return of the King, I just kept mentally cursing and scolding myself for not seeing them when I was a kid. Easily, the greatest movie trilogy I've ever seen.

Edit: Also, I want Into the West to be played at my funeral.

Lord of the rings without a doubt. I have the theatrical cut on DVD and extended cut on Blu-ray, very much enjoyed the 11 hour extended cut and watched the whole extended cut again with commentary track.

Unfortunately the Hobbit trilogy sits at the bottom of that list.

Probably not all of them the best, by certainly my favourites:

Dollars trilogy (A Fistful of Dollars; For a Few Dollars More; The Good, the Bad and the Ugly)
Mad Max (Gibson's)
The Godfather (though 3rd was quite weak)
Back to the Future
Before (Sunrise, Sunset, Midnight)
Austin Powers

Cornetto Trilogy hands down.

Can't believe I forgot Austin Powers. Great shout, even if the third one isn't that great.

Which cut is better? I've heard conflicting things. I am going to watch them for the "first time" (seen them before but was far too young and my attention span was fucked). 

The theatrical cuts are better paced and edited, but the extended cut contains plenty more great footage that helps round out the story. I think the theatrical cuts make for better first time viewing, then any fans should definitely check out the extended cut after.

Probably a toss up between Back to the Future and SW. TLOR is really great, but some of the changes made from the source material just had me scratching my head and saying, "What was the point in that change?"