Around every 7k miles when I change the oil in the Sonata.
The Jeep I've lost track of the rotations, the tires are getting older and I don't drive it all that much, I don't think I'll rotate them anymore. I will when I get new tires in a year or two.
Depends on the vehicle. I had a Crown Vic I bought with cheap tires on it, had to rotate every 5k or less tokeep the front edges from getting bald. Had an early 2000s Wrangler with a 4 cyl, and it went around 15k between rotations.
Every 10K miles. I used to do it every 5K and then I realized that I end up buying tires based on age like JHZR2 as well. I put 12-15K miles per year on my cars anyways, so after 5-6 years buy a new set despite having 30-50% tread still left.
I try to do tire rotation on the same schedule as oil changes, so every 7500 miles. However, the winter tires kind of throws a kink in the plan.
Regular rotation has paid off big on a couple occasions when I have gotten warranty on tires that have worn out prematurely. Being able to prove that the tires were rotated on a regular basis makes the warranty claim much easier.