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 RTF was introduced a while back by Microsoft, but has since been superseded for the widely adopted HTML; even Outlook 2007 now defaults to HTML.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).

In Outlook, on the Tools menu  ...