Do you have your email accounts set to download headers only in Outlook? Also, what protocols are your email addresses using, i.e. POP3, IMAP or MAPI? Are messages that do not open automatically arriving via one sort of protocol (or in particular accounts) and the problem emails via other protocols (or other accounts)?

If you don't know the protocols being used, open Outlook and click Tools - Options, select the Mail Setup tab, then click E-mail Accounts. The protocols in use are listed to the right of each account. Ignore the /SMTP bit, that only has to do with sending, not receiving.