Building curved walkways softens the landscape by counteracting rigid lines (a rectangular house, a straight driveway, etc.). If the walkway cuts through an area with great visual interest (for instance, a variety of garden and flower beds, shrubs, trees, statuary, water garden, rock garden, etc.), building a curved walkway makes more sense than a straight, no-nonsense walkway. You'll want to meander through such an area, slowing down to fully appreciate its treasures.
But don't go crazy and build all your walkways or pathways curved, indiscriminately. It depends on the function of the walkway. If you're building a utilitarian walkway (such as providing a path for you to haul groceries in to the house from the car), you will normally want to build a straight walkway.