Or you can modify the php code to display it in the table. Open admin/categories.php and search for this function:
function show_category_rows($cid = 0, $depth = 1) {
Inside that function and below this line:
show_text_link($lang['add_subcategory'], "categories.php?action=addcat&cat_parent_id=".$cats['cat_id']);
Replace:
echo "\n</td>\n<td align=\"center\">";
with:
echo " CAT ID: <b>".$cats['cat_id']."</b>\n</td>\n<td align=\"center\">";