Frequent tipster Leonid Nemirovsky shares a method for making borders in AutoCAD table cells "invisible."
"To make borders between cells in a table disappear (for example, when you need to merge cells, but can't do that in order to save cell content), just make these borders color 255 so they will not print."
Notes from Cadalyst Tip Patrol: There are a few ways one can display a table cell border — or not display it, as the case may be. Set the color of the border, as the tip here suggests, to match the color of the paper the drawing will be printed on. If you are not using a CTB file for pen settings, then color 255 is very close to white, which will work as long as you are using white paper (which most of us do, I assume). You can also use the true color of 255,255,255 which is white.
Another method is to turn the borders off. Select the table you want to change, select the cell, right-click and pick Borders, then click the No Borders button. This will turn off all of the borders for your selected cell or cells. You can then turn on individual borders by clicking the appropriate border icon, no special layers or colors needed. You can also change the color, linetype, or lineweight of the borders this way.