22 Frames collects captioned videos from throughout the Web. The site also says they are specifically working to help make it more useful for English Language Learners.
You wouldn’t be able to use the site directly from the Web in most schools, since content filters block most of the popular video-hosting sites. But you might find videos worth showing in other ways (see The Best Ways To Access Educational YouTube Videos At School).
The Make Use of blog has a more lengthy description of the site.