Convert Microsoft Word .doc to .docx ?

Can Hazel (help to) convert Microsoft Word files from .doc to .docx format? When I download a .doc file, I would like to have it converted to .docx (and preferably have the .doc file deleted). Can this be done with Hazel? Thanks!

Hazel can't do the conversion itself. You'll have to find some other program to do that part. Hopefully it something that you can trigger from Hazel but that is dependent on the program in question.

Thanks, Mr Noodle! Does anyone know if it can be done programmatically within Word (macro, script, etc.)?

Look into AppleScript. I don't know if Word is AppleScriptable but searching around various AppleScript sites should give you the answer.