In my backyard in Michigan, you could burn whenever you wanted, but the flames had to be less than six feet tall.
The small town I grew up in Kansas had "burn days" in the fall that were supposed to generally for burning leaves. The bay area has "spare the air" days where you can't even use a fireplace or charcoal grill.
I'm guessing it's usually banned our regulated by local law.
Which gets me wondering, where do people generally find obscure laws like this? Like my goofy neighbor told me the six foot flame thing, I never attempted to verify it in any way.