Someone already mentioned the Star Wars trailers have tons deleted footage. Specifically, the ESB trailer features shots from the deleted Waampa subplot, a steamier kiss between Luke and Leia, and a shot of Lando running to an elevator among others.
In the first trailer for Attack of the Clones Anakin says something like "I've learned this lesson before," and Obi-Wan replies "You haven't learned anything." I never saw that in the movie.
Star Trek: Generations shows clips from the original intended ending that they decided to reshoot since it was not well-received. Not that they did much better with their new ending mind you, but the original is there in the teaser.
To add to Peter's comments about Generations, there's a clip in the final theatrical trailer of Kirk saying to John Harriman on the bridge of the Enterprise-B, "Let's try to cheat death together." That was also included in some of the TV spots as well, and there was even an alternate angle of Kirk saying, "The 24th century is not so tough!" that was used in one of the TV spots.
Other notable examples:
Superman: The Movie - An alternate angle of Kal-El's starship on Earth is used, along with a brief clip of Christopher Reeve as Superman. That clip was from the Superman/Jor-El discussion that was not seen until 1994 in the KCOP telecast of the extended version and until 2001 in the SE DVD.
Superman IV: The Quest for Peace - This one's rife with extra footage that didn't make either the 90-minute U.S. cut or the 93-minute European cut, yet are present on the trailers. Check out the DVD for two such scenes that were included, as well as the Multimedia section of www.capedwonder.com for a recently discovered trailer loaded with several unseen clips.
Star Trek: Nemesis - One of the most prominent scenes used in both trailers that didn't make the final cut was of Shinzon's assault on Deanna Troi in the turbolift, particularly him saying, "Don't fear." That latter clip was not in the film, yet segments from this sequence is on the Nemesis DVD.
I seem to remember some of the Batman Forever trailer having stuff not in the movie. Tommy Lee Jones's Two-Face saying something like "If the bat wants to play, we'll play!" My brother went around saying that for the next few months, except I don't think it even ended up in the movie.
But, concerning Spider-Man, it was a scene only for the teaser, and never intended to be in the movie. In fact, this is only a joke for announcing the movie, I don't really can imagine Spidey with a giant web for capture the helicopter!
Tony Scotts movie Revenge shows a action scene with a horse and a moving train that isn't in the film. Supposedly the cut we saw was hacked to bits and the real film has quite a bit more material. I've been hoping for a special edition but one hasn't surfaced yet.
I was watching the "License to Drive" SE and the trailers show tons of clips of stuff that did not make the final film including clips of them smoking Dean's cigars in the Caddillac, Corey Haim spilling a bunch of crap from his locker in some kind of a rush, clips of the original ending that is shown on the DVD and some others as well.
Here's one nobody has mentioned yet. Tom Berenger delivers an absolutely hilarious line in the trailer for the first Major League film. That line, as much as anything else, made me go to see that film. Alas, I waited all through the film for that wonderful line, and it never came!!! I still can't believe that it was cut.
The deleted scene where Andrew confronts his dad in the bathroom can be seen in the theatrical trailer and internet exclusive trailer in the trailer for 'Garden State'.
The various trailers for The Lord of the Rings trilogy contain a number of moments not included in either the theatrical or extended versions of the films. From the FOTR trailers:
An uncompleted shot of the Ringwraiths (sans the blurring/windy effect) as they appear in the wraith world.
Gandalf saying of the ring, "It must be destroyed!"
A great shot with the camera tracking in on Legolas as he notches an arrow and fires, plus a shot of what could be the same arrow whizzing past Aragorn's ear (I believe these shots were from an orc ambush scene cut from the film).
From TTT:
An alternate, more emphatic, take of Aragorn describing the orc host: "Ten thousand strong!"
From ROTK:
Merry, to Pippin: "We will see the Shire again."
A nice shot of Elrond on a bridge at Rivendell.
That's all that comes to mind at the moment, but if I had the DVDs with me, I'm sure I could spot plenty more.
My favorite trailer scene not in the film was from Air Force One. Whenever Gary Oldman has Harrison Ford by the tie and has the AFO phone on the other hand and screams, "You can finish this with one phone call!" Just the intensity of Oldman is great. Of course, not in the movie though.
Also, Titanic has a ton of scenes in the trailer that weren't in the movie that will hopefully be on the 4 disc DVD coming out soon.
Add to this an alternate (and better, IMHO) take of Aragorn's "this day, we fight!" speech. It was weird hearing him say it in a different intonation in the movie.
Patriot Games: The dialog from the scene where James Earl Jones visits Harrison Ford to tell him that Sean Bean has escaped is different in the trailer.
I know. Would probably have been the best line in the whole picture.
The trailer for "Who Framed Roger Rabbit" contained some of the deleted "Pig Head" sequence...
also, I didn't see this movie... but I got a complaint about it when I worked at Regal in High School...
In the trailer for the movie "Good Burger" Garret Morris walks in and asks for a "Good Shake" and Keenan reaches across the counter, grabs him by the shoulders and proceeds to shake him.
Yes someone complained after the movie to try and get a free pass because they paid "specifically to see that scene"