It sounds like when the emails are downloaded to the Blackberry, it's telling the server that they've already been read. 

What kind of Blackberry are you using?

It is a Blackberry Bold (my father's old phone).  And yes, that is exactly what it is doing.  As soon as the e-mail is received by the Blackberry, whether I have viewed it or not, it shows up as read in my ATT mail.  And it's driing me nuts!  Any help you could provide would be very appreciated!!

I did a bit of research and it looks like this is expected behavior for the Blackberry. This support article from Blackberry says the following:

Wireless read and unread Status

Email messages marked as read or unread on the BlackBerry smartphone will also be marked as read or unread in the mailbox of an integrated email account. However, this does not apply to Post Office Protocol (POP) integrations. See the Additional Information section for information on what types of integrations support this capability.