Depends on your equipment and your property. Back when I was mowing as a side job and using my commercial walk-behind mowers, it was invariably back and forth. I alternated direction of the stripes 90 degrees each mowing; side to side one week, front to back the next. Some guys also throw diagonals in for a four week rotation. Keeps you from establishing wear patterns and just looks nice.
Now that I've dropped the mowing business, I use a JD garden tractor for mowing my own place. It would take forever to try to stripe everything, because of the big loop or three point turn at the end of each stripe. So now I compromise: the front part of my hill that is right in front of the house and easy to see from the road gets striped, even though it takes extra time. Everything else goes roundy-round, since it's quicker and the lawn there isn't good enough to show off striping anyway.