Type the word you seek in the find box. Below, you will see a drop-down button that says "Reading highlight." Press this and select "Highlight all." Word will then tell you, in the box, how many instances of the word have been highlighted.

Note, that the words will not, however, remain highlighted when you close or save the document; this is a temporary feature.

I am looking at Word 2007, but I am almost completely certain that the same feature was in the 2003 Find box.