Vbeachcomber,
iPhones do play .mov files that you might have in itunes, but over the web it usually boils down to the resolution that the video is in, also another issue could be the .MOV container format can store a variety of codecs. This is true for other containers like AVI or MP4, which is why one .AVI file will work in QuickTime, but another will prompt for a plug-in that it cannot find. Even if iTunes can recognize the container file, does not mean it can play the codecs stored in that file.