I first encountered this problem using Outlook 2013 connected to Exchange 2007. If the client is connected to the Exchange server in cached mode the problem occurs. Mail from clients on the Exchange server will not show contact photos in their email messages which of course assumes that you have added their photo to your contact list. Mail from external sources, i.e. not domain members, work fine. If you change the Outlook configuration to run in on-line mode (not cached) the problem will go away. This is a bug in Outlook 2013 for which Microsoft does not have a fix, only a "work-around". If you want to read the whole story including an excellent statement of the problem by Paul Hefford see this thread in the Office TechCenter Forum.
Contact photos not showing in reading pane in Outlook 2013
Contact photos not showing in reading pane in Outlook 2013