Ordinary household and construction debris is welcome. Minnesota's bans are what shape the rest, and they are stricter than most states.
Yard waste leads the list. State law has kept yard waste out of mixed municipal waste and out of disposal facilities in the metro area since 1990, so grass, leaves, and garden trimmings cannot go in a container. The City also prohibits depositing leaves on a public street, which closes the other obvious shortcut.
Major appliances are banned too. State law says a person may not place major appliances in mixed municipal waste or dispose of them on land or at a solid waste facility, so the old washer, the water heater, and the refrigerator all need their own route.
Televisions and monitors with a picture tube have been barred from the trash since July 2006, which catches a lot of basement cleanouts in a city with homes of this age.
Paint, solvents, fuel, used oil, batteries, pool chemicals, and asbestos never belong in a standard container either. Anoka County runs a household hazardous waste facility for most of that. Tell your account manager what the job will turn up and they will arrange the right route for it.