Radiocarbon, or C14, dating take alot of flack from various anti-science folks. Although it is mostly the target of creationists, other pseudo-intellectuals such as Graham Hancock have also taken pot-shots at it when it showed their preferred conclusions to be bullshit. I find it telling that radiocarbon dating takes all of the heat, because this fact reveals the true depth of the ignorance of the creationists and pseudo-archaeologists. To explain why will require a little bit of background.
Radiocarbon is only one of many forms of radiometric dating, others include potassium-argon dating and uranium-lead dating. Radiometric dating is based on the principle of radioactive decay. Radioactive atoms decay by expelling particles from the nucleus, thereby becoming other types of atoms (carbon 14 decays into nitrogen 14, for example). By examining the proportions of elements within a sample and comparing that to the decay rates of the radioactive isotope, you can arrive at an age for the object in question that is accurate within the parameters of the test being used.
Radioactive materials decay at a predictable rate based on well-known principles from chemistry and physics. So, once the half-life (the length of time that it takes for half of a sample of radioactive to decay) of an isotope is worked out, a dating method based upon that isotope can be developed. It is important to emphasize that radioactive decay curves for isotopes are based on well-known principles, because there are numerous people who like to claim that the decay curves are either poorly understood or just made up, when they are in fact very well understood and rigorously examined.
The radioactive isotope has to enter the material being tested somehow, obviously. The way that this occurs varies by material type, but for radiocarbon it is due to organisms absorbing it from the atmosphere, whether through respiration or through eating organisms that have absorbed it. Once the organism dies, it no longer absorbs Carbon 14 and the decay can be measured to determine time since death. Radiocarbon only works on organic substances, as it is living things that absord the Carbon 14 in predictable ways, but other forms of dating that rely on other radioactive isotopes can be used on other substances - you wouldn't use radiocarbon on rocks but potassium-argon dating may be appropriate, for example.
Paying attention to a method's parameters is important, as young-Earth creationists will often point to the method being used on a sample that is either much to young or far too old for the carbon 14 procedure, and then claim that this "proves the failure" of C14 dating when the reasons for the alleged failure are due to basic principles of chemistry that the person claiming the failure ignored so that they could provide a false result (in other words, they're just a dishonest mutha'fucka'). It's no different than claiming that a 15-foot tape measure is inaccurate because it's not useful for measurements on the molecular level, nor for measurements on the galactic scale. Every tool has its limitations, and the limitations of radiometric dating are well understood by the people who use it.
Radiocarbon, specifically, is useful for dates up to 50,000 years ago (though some chemists argue that it can be useful for dates up to 60,000 years ago), while very recenet (such as within the last century or so) dates will show so little carbon decay that the margin of error is larger than the dates returned. So, if you're trying to figure out how old something is, and you have reason to believe that it is less than 100 years old or more than 50,000 years old, don't use carbon dating, just like you wouldn't use a tape measure to examine the output of the Large Hadron Collider or the distance between Earth and Alpha Centauri - it's not the tool that's flawed, it's the idiot who insists on using the tool inappropriately that's the problem.
Another thing to keep in mind with radiocarbon dating, specifically, is that the amount of C14 in the atmosphere has changed over time. Thankfully, based on a variety of sources ranging from geology to botany, we have a pretty detailed description of how C14 levels in the atmosphere have changed over time, and that description is becoming more refined and detailed all of the time. So, once we know how much C14 is in a sample, and work out the uncalibrated date, we then calibrate it by comparing it to what is known about C14 fluctuations over time, and we can work out the age of the sample.
Okay, so why does criticizing only C14 indicate ignorance on the part of the person doing it? A few reasons. As noted above, many of the people who wish to discredit it use it in inappropriate ways in order to make it look worse than it is. The tape measure to a distant star scenario, basically. In addition, the fact that C14 has come in for abuse but not other forms of radiometric dating is interesting, as it is usually creationists who attack C14 dating while C14 does not have a sufficient age range to account for the homonid fossils that they find so offensive (though it does demonstrate the reality that the world is more than 6,000 years old, which they also find offensive). In other words, the fact that they go after C14 and not other forms of radiometric dating indicates that they haven't done their homework, which indicates that they don't know what they're talking about, which indicates a rather astounding mix of arrogance and ignorance.
There is one other important piece of information, though. Radiometric dating is not the only form of absolute dating*. For other examples, we can look to dendrochronology (using tree rings to assess the passage of time), obsidian hydration (measuring hydration rims on obsidian that form after obsidian breaks), and thermoluminescence (the heating of materials to relase trapped electrons and determine the point in time when the materials was lasted heated to a sufficient temperature). All of these methods have their values and their limitations, and some of them are less reliable than radiocarbon, but none of them come in for abuse the way that radiocarbon does. This again implies that people who are worked up over radiocarbon dating don't know about other forms of absolute dating, which, again, imples that they haven't done their homework and don't know what they are talking about.
The basic point t this entry is this: there are legitimate criticisms of C14 and of over-reliance on C14, and C14 dating has it's limits. However, none of these legitimate criticisms ever comes from the creationists. Instead they rely on mis-characterizing C14, claiming that it is used for things that it is not used for, ignoring it's known limits, and their tactics indicate an astounding ignorance of the dating methods used in archaeology, paleontology, and geology.
*Absolute dating refers to methods that produce definite ages or age ranges for objects (i.e. it's between 5,000 and 5,300 years old), as opposed to relative dating methods, which only tell us how old things are in relation to other objects (for example, superposition: Object A was in a strata above Object B's strata, therefore Object B is older).