Left <-> right interchange doesn't really happen anymore since radial tires have become standard on most vehicles.
Radial tires are unidirectional, so if you go left -> right your tires will be rotating backwards, and then they won't be able to channel water out from the treads.
Change the wheel a given tire is attached to. This is to have a regular "wear" on your tires. Incidentally, you can also regularly rotate your mattress to have a better sleep.
I don't think I've ever had this done when getting my tires rotated. They just move the wheels and tires from front to back and sometimes from left to right.
* every 7,500mi: rotate tires
* every 22,500mi: change cabin air filter
* every 5 years: replace brake fluid
* every 150,000mi: replace battery cooling fluid
that's it. crazy!