I copied a video from my iPhone to my Windows/7 computer. It is 1080p, 24fps and encoded with H.264. The video plays without problem in iTunes and Windows Media Player, but there is only audio in Quicktime. I reinstalled Quicktime, but the behavior presists.
I figured out the problem and it is Quicktime 7.7.2. I opened the video file on a system with Quicktime 7.7.1 and it worked, then I downloaded the Quicktime 7.7.1 installer, deinstalled 7.7.2 on my computer and installed 7.7.1, and the video was viewable!