Contrary to what you might think from reading through this site, there is also another way of seeing a "widescreen" movie -- matted (or framed) widescreen.
Although it is true that many movies that are shown on a full TV screen have their sides cut off, it is also true that some movies do not have the sides cut off. In fact, some movies are shown with too much information.
When you watch a movie that was filmed in a "flat" or "spherical" method, that is with no horizontal ("anamorphic") compression, the top and bottom are matted out to provide the aspect ratio that the filmmakers intended. This is known as "soft matting". Most matted movies are matted to a 1.85:1 aspect ratio, although Super35 movies are most often matted to a 2.35:1 aspect ratio. When such movies are displayed on TV or in a non-widescreen manner, the top and bottom mattes are removed. The result is that you see more of the frame than was intended although there is normally a small portion cut off the sides as well.
For the most part, only live-action scenes in Super35 movies have the mattes removed. Super35 scenes with special effects are hard-matted at 2.35:1 and must undergo the pan-and-scan process to fit the screen, thus resulting in a loss of about 45% of the original image. Some newer Super 35 movies reformat special effects scenes to add extraneous information to more adequately fill the screen.
The live-action image on the right is from James Cameron's Terminator 2, which was filmed in Super 35. The red outline shows the part of the frame was originally shown in theaters. The blue frame shows what is seen on the non-widescreen version.
Although this might seem to be a benefit to those who do not like widescreen, keep in mind that not only are scenes with special effects subjected to the pan-and-scan but there are also many instances where seeing too much of the frame can provide very interesting bloopers that can ruin the intent of the scene.
The compilation above is an example from the classic comedy (and one of my favorites) A Fish Called Wanda. In this scene, John Cleese is supposed to be naked when suddenly - and unexpectedly - a family walks in. The picture on the left shows the scene in its intended, matted aspect ratio of 1.85:1 and does indeed give the impression that he is naked. The picture on the right shows the same scene in a "full frame" format where the mattes are removed. As you can see, he's actually wearing shorts, thus dramatically reducing (if not eliminating) the intended comedic effect of the scene.
Another problem that arises from watching soft-matted movies that are displayed in a full frame is that you often get a chance to see equipment that you were not meant to see, such as boom microphones.
The example on the left demonstrates this. This is an image from the original late-1980s VHS release of The Princess Bride, another one of my favorites. As you can see, the mattes have been removed; but as a result, you see more than the trees. The blue circle shows the boom microphone that was exposed when the mattes were removed.
(This little faux pas was corrected for later VHS and DVD releases; however, I was fortunate enough to buy this video when it first came out, and I also happened to notice the boom mike the very first time that I watched it. So, don't bother pulling out your DVD to look for it. I do believe that Twentieth Century Fox has "corrected" this little mistake.)
If you want to see the problems with viewing "full frame" open-matte films in action, you can see the scene mentioned above from The Princess Bride in my Multimedia section.
The removal of mattes for "regular" TV viewing also violates the principles of the original aspect ratio because what you are seeing is not what the filmmakers wanted you to see. These examples show that just because you can see more of the frame with full-frame, soft-matted movies does not mean that you are seeing what you are supposed to see. Even if you are actually losing visual information with soft-matted, widescreen movies, the widescreen version is still the only way that movie should be seen.