Other than sentimental reasons, why do folks still use the square grid?
Old habits are hard to break.

Of the three major grid types (square, staggered square, hex), which one do you prefer? Why?
Hex shaped would be my main choice as it gives more choices for smooth movement, the 12 facings and better sense of front, back, sides.

Now take the game system out of the equation and tell me which one you prefer? Why?
I'd prefer none at all, instead using overlays and ruler type tools.

Did you know that with Virtual Tabletops such as MapTool that you can actually play without any sort of grid because it is able to measure distances?
I'm actually looking forward to doing the same with Viewing Dale. Using a ruler overlay to measure distances, for that true table top feel.