There are two schools of thought on this subject. Rotating the tires, which is recommended by all tire manufacturers, involves changing their position on the vehicle from one wheel location to another. This helps to even out tire wear between all the tires so the tires last longer and do not develop abnormal wear patterns. This may be recommended every 8,000 to 15,000 miles.
On front-wheel drive cars and minivans, the front wheels tend to wear at a much faster rate than those on the rear. After 50,000 or 60,000 miles of driving, the front tires may be worn out while the ones on the back may still have half or more of their tread life remaining. By rotating the tires front to rear and side to side, differences in wear patterns between the wheel locations spreads the wear out and more or less wears the tires evenly -- or so the theory goes. Consequently, tires that would have lasted only 50,000 or 60,000 miles on the front of a front-wheel drive car may last 70,000 or 80,000 miles. But on the other hand, the tires on the rear that may well have gone 100,000 miles only last 70,000 or 80,000 miles.
Those who say rotating tires is a waste of time argue that it makes more sense to replace the front tires on a front-wheel drive car or minivan when they wear out, but to leave the back tires alone -- especially if you're putting a lot of miles on the vehicle or plan to keep it a long time. The back tires will probably last as long as two sets of front tires, so in the long run you end up buying the same number or possibly even fewer tires by not rotating. Plus, you've saved the time and money that would have been spent on rotating the tires.
This argument doesn't fly in the case of certain low profile performance tires that have a tendency to develop a heel-and-toe wear pattern if left in the same wheel position too long.
For rear-wheel drive cars and trucks, the recommended tire rotation pattern is to rotate the front wheels to the opposite side on the rear, and move the rear wheels to the same side on the front.
For front-wheel drive cars and minivans, the recommended tire rotation pattern is to rotate the rear wheels to the front on the opposite side, and move the front wheels to the rear on the same side.
If your vehicle has "directional" tires (small arrows or triangles indicating the direction of travel), the wheels must not be switched side to side. They can, however, be rotated front to rear on the same side.
If the front and rear wheels and/or tires on your vehicle are of different size, then rotation is out of the question.