Most household and building debris can go in. California's trash bans and the City landfill's own list set the limits.
California's recycling agency, CalRecycle, lists the waste banned from the trash statewide. It includes all batteries, fluorescent lamps, TVs, computers, monitors, and printers. It also includes paint, solvents, pesticides, motor oil, antifreeze, tires, asbestos, and treated wood.
The West Central Landfill won't accept antifreeze, asbestos, batteries, fluorescent bulbs, gasoline, liquids, oils, paint, or pressure-treated wood. Hazardous waste, solvents, and fuel of any kind stay out of a standard dumpster, too.
A few items are simply billed by the piece. The landfill charges for tires, mattresses, couches, and appliances one at a time, and fridges, freezers, and air conditioners cost more than other appliances. It takes TVs and computer monitors at no charge, so drop those off separately instead of loading them.
Ask your account manager about anything you're unsure of before it goes in the container.