There are instances when tire rotation is not proper. For instance on vehicles with unidirectional tires and different size tires front to rear. In this case the tires are not rotated at all. Other cases could include, when one tire is a different tread pattern or newer than the other three. This can result when one tire is replaced, perhaps due to tire damage. Mismatched tires on the front can result in the vehicle pulling in one direction. In such a case the odd tire is placed on the rear and left there.
In cases where only two new tires are installed, they should go on the rear of the vehicle. If the vehicle has two much newer tires on the rear, they should not be rotated.
Pattern 2, front tires moved to rear
Putting the front tires on the rear and rear on the front is very common practice. The left tires remain on the left and the right remain on the right. This method is necessary with unidirectional tires or wheels. That is tires and/or wheel that are different from left to right. This method also offers the advantage of revealing on which side of the vehicle a problem may exist.
Patten 3, cross the front tires to the rear
Many people still believe that crossing radial tires, side to side will cause damage. This is not true, and cross-rotation is sometimes recommended by manufacturers. Cross-rotation can also help when tires are worn irregularly, such as being chopped in spots. This method cannot be used with unidirectional tires.
Crossing the front tires to the rear may help with slight uneven wear on front tires. Severe chopping and wear will not be corrected by tire rotation.
Pattern 4, cross the rear tires to front
A slight variation on pattern 3. The rear tires are crossed to the front, rather than fronts crossed to rear. Some manufactures recommend this pattern. It can be useful when the rear tires become slightly chopped or worn in spots. Again, severe wear or chopping will NOT be corrected by tire rotation.
Tire rotation can also cause an increase in tire noise, especially when tires are worn or chopped. For instance, a chopped tire from the rear may be more noisy when placed on the front. The only true remedy for excessively worn tires is replacement.
Tire inflation and proper wheel alignment are also very important to tire life. For more information please see the AGCO Automotive Detailed Topics on Tire Inflation, The AGCO Way and Wheel Alignment Myths.