How can I merge two table columns in Word 2003 or Word 2010?
Do you mean merge 2 (or more) table cells into one table cell, or merge the contents of 2 (or more) cells into a 3rd cell (aka concatenation)?
If its the 1st option then simply select both (or more) cells together, right click and select
If its the 2nd option then I don't think this is directly possible using Word table formulas - AFAIK you can only do numerical calculations.
You can write a macro which loops through all the rows in the table and takes the contents of columns 1 and 2, concatenates them and enters the result in column 3. This article may be a point to start from.
As an alternative, I would suggest copy/pasting the table into Excel, using Excel's CONCATENATE function and then copy/pasting back into Word.
If you erase the column border with the Eraser, it merges each pair of cells just as you would expect. Eraser is under Table - Draw Table in Word 2003.