When you yourself are sending out e-mail to others, your recipients might complain about them not being able to open this e-mail. This is because you're probably using Outlook (with Exchange) and are sending e-mail in RTF-format.
Using RTF in a mail is generally a bad idea, because it's not an internet standard for e-mail layouting. RTF was introduced a while back by Microsoft, but has since been superseded for the widely adopted HTML; even Outlook 2007 now defaults to HTML.
So, to get rid of the winmail.dat, simply set your mail format to HTML (instead of RTF).