What time period can carbon-14 dates have?
Carbon 14 has a half-life of 5,730 years, and thus it can be used to date very precisely a large majority of things, particularly wood and so on.
It is only not useful for very old things where all the carbon 14 will have left, or almost left - and for these there are other isotopes of previous elements, that can be used with a much longer half-life.