Most household and remodeling debris is fine. Illinois law and the facilities that take your load set the limits.
The Illinois Environmental Protection Agency says state law prohibits landfilling many common electronics, including TVs and computers. State law also bans used or waste tires from landfills. Keep both out of your container.
Hazardous waste, liquids, paint, solvents, fuel, gas cylinders, and asbestos don't belong in a standard dumpster either.
For the electronics and household items you pull out, Kane County's recycling center in Geneva is close by. It charges small per-item fees for TVs, monitors, alarms, aerosol cans, and a few other items, and takes many others for free.
When you're unsure about something, ask your account manager before it goes in.