Do you use any other mail apps? For example, on your desktop, fetching from same accounts over POP3?
Most mail services will mark messages as read when you do this.
What accounts are these? Gmail? Yahoo? Outlook.com? Something else?
Feel free to contact me at kmansoft / gmail, and I'd appreciate a debug log:
Long press the account, choose last item (Diag: message dates). On the next screen, choose the Inbox folder (if there is a control for it -- there won't be for POP3), run the test to completion. At the end, the app will offer you to email me the log.
