Should people with myopia (short-sightedness) who otherwise show no symptoms of eye problems and wear corrective lenses visit an eye doctor (whether optometrist or ophthalmologist - my country doesn't even have that distinction)? If they should, are there any recommendations as to how often these visits should happen and what exams need to be scheduled?
This probably varies from country to country. In mine (France), it is recommended to see an ophtalmologist (we have the distinction here) every three years for non-severe myopia, because your sight can vary a bit during that time. For children it's every year because children's sight vary much more than ours. For severe myopia, the ophtalmologist decides what schedule will be best - often every year as well.
The tests are generally eyesight measurements (for myopia, far-sightedness and astigmatism). Sometimes, especially in older people, you'll get a fundus examination as well.
This site has description of myopia progression that justifies the regular checks in the classification part.