Let me see.........we have TV's, Microwaves and now fire detectors in our homes with just a little radioactive material. What next? It's starting to add up.
Actually, you might be surprised at the household items containing radioactive material. We once held a geiger counter up to some china dinner plates and the thing went nuts. Be careful what you look for, eh?
As for smoke detectors, a colleague of mine used to use one to calibrate his detection equipment.
All that said, there's three types of "radiation:" alpha, beta and gamma. The really bad one is gamma; alpha and beta radiation is not that bad, but is still called 'radiation.' Even gamma radiation is a very broad term, as it refers to any "light" of higher frequency than x-rays.