Films that come to mind include:

Disney's Brother Bear
Brainstorm

are there any other films that switch from one aspect ratio to another for dramatic effect?

Galaxy Quest

Kill Bill Vol. 2 - When The Bride is being buried alive, the aspect ratio switches to 4:3 for a short time to make things a little more claustrophobic

Matinee. A majority of the film takes place within a 1.66:1 frame, but switches to full on 2.40:1 when clips from the films the characters are watching are shown.

Dr. Strangelove

The Road Warrior

The intro is 4:3 and then it widens for the opening shot.

wasn't this done in 3 different aspect ratios?
1:66 for the old tv parts
1:85 for the normal movie scenes on earth
2:35 when they go into outer space

This is something that was lost from the movie on DVD, I remember watcing this in theaters and i thought it added a great touch.

Why did this movie work, i remember watching the preview and thinking that it would only be okay, boy was i wrong cause i hadn't smiled that much at a movie in a while

It was probably 1.33:1 for the old TV shots, and according to the IMDB trivia page:
Yeah, they definitely need to get cracking on a sequel to this. It would be too much fun to see these guys again.

"The Horse Whisperer" started out 1.85:1 for the early scenes in New York, then switched to 2.35:1 when the action moves to Montana or whever Robert Redford's character lived.

in the NC-17 version of natural born killers, one shot in a shootout in the jail, is at 1:33;1.

Didnt Croc Hunter: Collision Course have different ratios when they would switch from film to documentary type camera? Seems like it did when I saw it in theatres.

Superman: The Movie opens with a 1.33:1 shot of the comic book and Daily Planet, then opens up to the full 2.35:1 for the opening titles and remainder of the movie. The 1.33:1 shot is stylized to look like an old tv program.

Don't the three "That's Entertainment" films switch from one aspect ratio to another all through their duration?

Bad Education

1957's Around the World in 80 Days.

Actually, that opening sequence is more an homage to the old movie serials (if I remember correctly, they did a couple of Superman movie serials before the famous 1950's TV series came out).

really?! I didn't remember that film having multiple AR's

yeah. I thought of this immediately. It was more noticable in the movie screen (saw it twice) than on a tv.

More American Graffiti was shown in 2.35, with 4 different storylines each in a different ratio- one at 2.35, one in about 1.85 with matting on the sides, one about 1.33 I think, and the other with split-screens and weird effects.

In theaters, was the movie shown in Matinee letterboxed, or did theaters actually show that at 2.35 with matting on the sides? That was one of the first laserdiscs I rented and that was 1.85 with the movie clip at 2.35.

Raging Bull switches to both full screen and color during the home video sequences, right? Or maybe I'm just crazy..

Heavenly Creatures.

as I recall, of course I could be wrong, but when I saw this in the theatre: White Flint Mall to be exact, I thought the set aspect ratio was 1.85 with the film clips 'letterboxed'.

Crooklyn
Everyone in the theater (Including myself) thought the projector had screwed up when the family goes out of town. Clever going there, Spike.

I double-checked this. On DVD, in the widescreen version, the fullscreen excerpts are shown fullscreen (with pillarboxing) most of the time, except when the camera zooms in on them for magnificent effect in 1.85:1 (as in the "A Pretty Girl is Like A Melody" number, from "The Great Ziegfeld") to make a point about what a scene like this would look like today, if we could afford to film something like it. In the fullscreen version of the DVD, those excerpts are wisely left in their original ratio throughout.

Yes. I didn't notice at first, but scenes representing the film within the film are different from the present day reality scenes.