For Outlook 2007 you're out of luck.  See http://office-outlook.com/outlook-forum/index.php/m/561201/#msg_561201 for more information.  You could of course save the email out as an HTML file on your hard drive and print it from there.  If you have a lot of emails to do this with, Attachment Save (http://www.SperrySoftware.com/Outlook/Attachment-Save.asp) can save the emails as HTMLs in one swoop.  You still have to print them, but you can select them all and then right click to print.  
 
  For Outlook 2003 though, you can go to Tools…E-mail Accounts…View or change existing e-mail accounts…choose your account then select Change…and under Your Name (in User Information) erase your name.  Note that you cannot leave it blank and that you must have some value there (a department name or company name for instance).  Leave the other settings alone and click Next, then Finish.  You can now print with your new text appearing in the bold line above the email itself.