If you used Word 2013 I think you wouldn't have any problems, but I'll assume that you've made a mistake and you have Word 2003 :) in such a case you may indeed have problems opening docx files. That extension has been introduced in Windows 2010. To open it you can:
- use Docx Viewer - this free application allows you to browse DOCX documents (but you cannot edit them)
- install Microsoft Office Compatibility Pack - this package adds additional features to your Office, allowing you, among all, to open docx files in Word 2003.