Hmm...I've never run across this problem, so I probably can't help, but I'm going to assume that answers to the following questions might help the troubleshooters.
Who is your mail service provider? (and if you have more than one account, does it happen with all or just one/some of the accounts?)
Are the accounts this is happening to IMAP or POP accounts?
What's the nature of these emails...could they be similar spam type emails or are they emails from friends/coworkers that you know you've received/read previously? (Also, any patterns in these emails...are you receiving all your old emails or only ones from certain addresses/or domain names?)