A couple of years ago, I wrote a post about preventing Internet Explorer and Media Player from pinning to the taskbar. It was a fairly simple solution, and the post continues to generate traffic to this site. Unfortunately, though, the methodology died with the Windows 7 era, and none of the advice even applies anymore. I considered updating that post with this new information, but decided this would better serve.
This method is, unfortunately, a bit more intrusive. It does, however, have the advantage of actually working. It will suffice not only for IE and Media Player, but Explorer.exe as well. My old post might work better for you if you’re on an older Windows. Should those steps fail you, though: these will not.