Well, I now map without a grid. However I play in maptool with the grid turned on because players like to know where they are, who they are flanking and like having an easy way to eyeball spell area of effects. Also, maptool currently works better with the grid on than off.

However, my slavish addiction to the rules will not extend to the 4e rule that the diagonal of a square is the same as the length of a side. A square is not a circle and I don't find non-Euclidean geometry to be 'easier' (waits for 4e flame war to derail mapping thread...)