If this happens on Windows systems it is because the Windows Photo Viewer and Live Photo Gallery may ignore the EXIF orientation of the photos. This data tells the viewer which way is up.
This is a Windows problem NOT an Apple problem. See here for discussion and details from Microsoft on how this may be fixed on Windows:
http://answers.microsoft.com/en-us/windows/forum/windows_7-pictures/windows-phot o-viewer-or-live-photo-gallery-does/a161c8da-c1ce-4347-a92e-724f9e535c15
You can also avoid this problem by taking photos in landscape mode with the iPhone/iPad held with the Home button to the right. In portrait mode keep the Home button down.