What are the rules for "Tax Free" income?

I've heard so many differing "facts" about tax free income in the middle east. One thing I'm pretty sure about, the US gives you 91K and change without taxing it. What I'm unsure about is the residency rules. Some people say 11 months in country without leaving, others 330 days out of a year. I read somewhere it has to be a calender year.

If anyone has a link to a factual guide, I would be very grateful.

35 days out of the US otherwise the "tax man" gets you