"it becomes odorless (by paralyzing your sense of smell) right around when you need to start getting worried"

I don't know if this is still the case in this litigation-happy age (probably not), but when I was in high school it was a common beginner's chem class experiment to make small quantities of H2S.

My physics teacher once commented that he hated it when they did that, because he'd smell it for a while, then not smell it any more -- leaving him to wonder whether it'd just gone away, or whether people were going to start keeling over.