In Word 2003, the 'Borders and Shading' dialog box controls the printing of the table borders.
From the 'Table' menu select 'Table Properties'. In the 'Table Properties' dialog box select the 'Table" tab and then the 'Borders and Shading' button. In the 'Borders and Shading' dialog box select the 'Borders' tab. On this property sheet, selecting 'None' will gray out the table borders and not display them in 'Print Preview'. Selecting 'All' will show the borders in both the display and 'Print Preview'.

Barry