Why do so-called "widescreens" display widescreen movies with black bars on the top and bottom?

Supposedly the entire purpose of a widescreen display -- be it a TV set, computer monitor or PlayStation Portable -- is to eliminate the black bars on the top and bottom of the screen. But in every experience I've had with one of these "widescreens," the offending "black bars" are still apparent as ever, just as though I was watching a standard 4:3 television. Can somebody explain this paradox?