In Asia (and Russia) (probably many other places, too), "squatty potties" are popular. They are a hole in the ground but with plumbing. Of course, there's always the traditional outhouse, but squatty potties smell better. Some people always use the squatty potty and, when one is not available, will squat on the traditional toilet "throne" by standing on the seat.
I believe some people have a stool in their bathroom to put their feet up in a close simulation to squatting.