In Italy it's, for low urgency, ~6months in public hospitals, 3days - 1week in private public-affiliated clinics paying the same as in the hospital (which are the main used solution to not overcrowd hospitals), <1day in full private clinics paying a bit more (eg ~ 80euros for a low abdomen eco, instead of ~ 15 in the public and affiliated)
If you have an high priority you get served by an hospital the same day.
How long do you wait for medical stuff? In Poland wait is sometimes >1 year
Depends on what you're looking for. A few years back I was told there was a 6-9 month wait at UCSF to see a GP that was willing to accept new patients. Non-urgent stuff like ultrasounds were around a 3 month wait.
If you have an high priority you get served by an hospital the same day.