Since the Fahrenheit and Celsius temperature scales were until recently both defined with respect to the freezing and boiling points of water at Standard Temperature and Pressure, the freezing point of pure water ought to be exactly 0° C or 32° F. At first, the Celsius scale was defined that way, while the Fahrenheit scale also came to be defined as having water freeze at 32° and boil at 212°.

However, nowadays units are defined in terms of SI quantities. A Kelvin is defined as 1/273.16 of the "thermodynamic temperature" of the triple point of water. 273.16 K is also defined as 0.01° C, and a Celsius degree is defined to be equal to a Kelvin. See this website and the NIST Units pages.

So, to answer your question, under certain conditions the freezing and boiling points of water will not be exactly 0° or 100° C. But they are close enough that we usually check our thermometers that way!

Dan Berger