Should you rotate or flip your mattress? The answer is that it depends. How often you need to rotate or flip also depends on the kind of mattress. Some mattresses do not need to be rotated and the majority these days do not need to be (and indeed shouldn't be) flipped. Others need to be rotated more often to ensure longevity and comfort.
The primary reason to rotate your mattress is to extend its life by evening out wear. In the past, the recommendation was also to flip your mattress, but with most modern mattresses this is not only not required but not recommended.
Instead, you can rotate your mattress by making the head the foot and vice versa. This means that the area where your hips and shoulders rest, which tends to create sagging, moves. This extends the life of your mattress and improves your comfort by keeping the support even. When you sleep in the new position, you will reshape the mattress, allowing the part rotated away to recover.
Classic innerspring mattresses are reversible or double-sided, especially older ones. These should indeed be flipped, which will delay the inevitable of springs poking through the padding by quite a bit. However, most modern mattresses are now one-sided.
With modern innerspring mattresses, there is no padding on one side of the mattress, just the springs. Foam mattresses are made in layers, with the lower layer being thicker and hotter. You should not flip these either, because you may damage them and they will be less comfortable. Obviously, pillow top mattresses should not be flipped.
So any mattress that is less than several years old should not be flipped unless it is an innerspring that is specifically labeled as double-sided. A few mattresses intentionally have different sides...for example, a mattress with a cooling layer might be designed to be used with the cooling side up in the summer, and then flipped to the other side in the winter. Other mattresses might be intentionally designed with a soft side and a firm side, so you can pick the one which is best for you.
Some mattresses are not designed to be rotated. Comfort zone mattresses are designed to provide different levels of support to different parts of your body. Rotating a comfort zone mattress will inevitably make it less comfortable.
Check your manufacturer's label to see how often they recommend rotation but as a general rule, most mattresses should be rotated once or twice a year, and older mattresses may need it more often. Every six months is thus a good idea.
If you have an adjustable base, you should rotate your mattress more often because otherwise it will sag where the adjustments happen. Adjustable air mattresses ("number" beds) should have the pad rotated frequently to reduce sagging. Pillow top mattresses should be rotated frequently, ideally every few weeks, for maximum comfort and lifespan.
Always get a second person to help; don't try to flip or rotate a mattress on your own due to the size and bulk. You could potentially injure yourself and/or damage your mattress. (This does mean that people who live on their own should consider a one-sided mattress that never has to be flipped).
Rotating or flipping your mattress does extend its life, usually by a year or so. However, not all mattresses are meant to be flipped or rotated. It's vital to check the care instructions provided by the manufacturer so that you know what the ideal schedule for flipping or rotation is. Following these instructions will help extend the life of your mattress and ensure a good nights' sleep.