Make sure you don't have low-bandwidth mode enabled for the account. If you use IMAP instead of POP, make sure you also don't have "do not download attachments" checked. Look on the "incoming" tab in the account's properties.
Otherwise, you'll have to right-click on a message and choose "fetch complete message".
Also, click on the wrench icon at the top right of Opera Mail and make sure "prefer plain text" is unchecked.
If this is only happening for a certain contact, you can fix it for the contact. For a problem message, click the from address in the header bar and then adjust the settings.
Also, you can close down Opera and edit operaprefs.ini (see "Menu -> Help -> About Opera Mail" and remove the "Suppress External Embeds" line if it's there. Or, just rename operaprefs.ini so Opera creates a new one (that won't mess with your account settings unless you have a custom mail folder location).