Where I am working everybody has to be certified. That includes everything from skid steer loaders to cranes. And also all of the other stuff like Hilti guns, confined space, fall protection etc.etc.
For all the OSHA 40 hr, HAZWOPER etc. we do it on line. The heavy equipment certifications are performed by a 3rd party.
A lot of municipalities are requiring certification too. Although in this case, I have only seen it enforced as a result of vindicitiveness on the part of the 2nd low bidder.