It’s almost always just related to standards of appearance. Landscaping, building modifications, having junk laying around, etc.
But garbage pickup was as far as I know managed by the county.
My HOA does. It mows lawns and removes snow. That's almost it: the rules are largely about not storing explosives in your house, which is apparently a thing in Wyoming.
Let me tell you about mine. Apart from snow removal and mowing the common lands, we handle curbside trash collection, repairs to water mains, flushing hydrants, maintaining streetlights (and paying for the electricity to light them), capital projects to manage stormwater, paving, sewer maintenance, installing fiber, forest management, etc. We also negotiate group rates for utilities like gas and electricity. A recent major project is replacing the pumps in our sewer lift station to the tune of $17k (an expense we budgeted for, thankfully). So yeah, apart from things like education and emergency services, we are basically a 19 house municipality.