iPhone supports the playback of open captions, closed captions, and subtitling. Captions appear onscreen just like the closed captions you see on TV. You can buy or rent captioned movies on the iTunes Store and sync them to iPhone to watch on the go.
The reality is that almost no shows or movies sold on iTunes contain closed captions. Since I cancelled cable I’ve bought quite a few shows from iTunes as well as a few movies. The only one I’ve found that included captions is Disney’s Alice in Wonderland. But ho! Apple says, “You can also create your own using a variety of tools and applications, including Compressor, one of the products in the Final Cut Studio 2 production suite (sold separately).”
Apple prides itself on its accessibility (as evidenced by the very fact that it has a page devoted to the very well-designed accessibility features of iOS). Why has not insisted that TV and movie studios include these captions? Nearly every show Apple sells through iTunes had captions at broadcast, and movies have them on DVDs, so it’s not like the studio would have to transcribe them again.