It is widely used in dating fossils or archaeological samples containing organic material such as wood, charcoal, bone, shells, etc.
It is sometimes thought possible to extend the dating range a few half-lives, so one occasionally sees dates as old as 70,000 years or more.
The Institute for Creation Research has a project called RATE, whose intent was to overturn radiometric absolute dating methods as evidence for an old age of the earth.
One of the arguments that they made was that diamonds contain significant levels of the radioactive carbon 14 (14C) isotope, indicating that they cannot be older than about 50,000 years old, and thus point to a young age of the earth.
While a number of Answers in Genesis (Ai G) articles related to radiometric dating have focused on discordant ages obtained from igneous suites (such as K/Ar dates obtained from volcanic flows, see last post), I have found that the most intriguing claims deal with the radiocarbon, or 14-C, dating method.
The reason is that Ai G authors do not simply try and persuade their readers to discount this method as wholly unreliable (even when the ages obtained exceed 10,000 years) but actually present the results as positive evidence for a young Earth.