I have version 2003 (hate 2007), so this may work for you:
Select the table (or the portions -- or cells -- of the table you want to affect). Click on the "Format" drop down menu at the top of the screen, and select "Borders and Shading." (Make sure the "Borders" tab is selected.)
There, you can adjust the width of any cell border lines (just the border lines, the cells remain), or eliminate them entirely. Experiment by clicking on the "Preview" portion of that tab, over on the right side.
(If you have the entire table selected, and want to eliminate all
border lines in your table, just select "None" under Settings on the Borders tab.)