Sounds like you're trying to paste in Plain Text (i.e., just the text, without any formatting). As far as I know Word 2003 does not have the capability to do that out-of-the-box. I recommend trying a little free app called PureText:

http://www.stevemiller.net/puretext/

You can set this app up to use any hotkey you want, and it will paste plain text into any program you want.

Hope this helps.

-SW