What do they look like?
See the example image below using Outlook 2003
Tested from Gmail to Outlook 2003, and Outlook.com and Yahoo mail back and forth with replies
Tested from Outlook 2003 to Gmail and Outlook.com and Yahoo mail worked okay (You have to View images)
Tested from the New Outlook.com to Gmail and Yahoo mail and Outlook 2003 with no problems at all
Tested from Yahoo mail to Gmail Outlook 2003 and Outlook.com with replying and everything worked fine.