It depends on the vegetable for me. I have done things a little differently this year. In order to preserve water, I planted some of my thirstiest fruits and vegetables in what I call the valley. I hope it doesn't backfire on me. I still mounded some vegetables.
I grew up on a large vegetable farm. There are many reasons to hill up potato tubers, but the most important one is that you don't want the tubers to come into contact with direct sunlight. It will turn them green and increase the potatoes' solanine levels.
@MartyR, I wish you luck and I hope you'll let us know how that works out for you. I'm curious about your results and might try it in the future.