The freezing point of water is generally said to be 32 degrees Fahrenheit (°F), 273 degrees Kelvin, or 0 degrees Celsius (°C). This is, of course, absolute nonsense.
Water starts freezing somewhere around 5 °C, and melting activity on the surface of ice has been observed down to -15 degrees °C. Zero degrees Celsius is just a good average approximating the point where the melting and freezing points of water stabilize, and things look settled on a macro level. They aren't; microscopic water droplets floating in the atmosphere can remain in a metastable up to -10 °C easily, and some may survive below -20 °C; this is known as supercooling, and under laboratory conditions with pure water and containers with no nucleation sites for ice crystals to form around, liquid water may reach about −48 °C (−55 °F) before freezing.
The actual freezing point is always a statistical average, trying to translate very active molecular events on the scale of nanometers into observations on the macro level. The three major factors that we large beings need to take into account are the aforementioned nucleation sites, impurities, and the local air pressure. Impurities are too large a subject for any one essay; however, for us humans the most relevant one is salt. Oceanic seawater usually freezes somewhere around -2 °C (28 °F), but you can add more salt and lower the freezing temperature, which is why people put salt on roads to melt ice. We also use a special class impurities called 'antifreeze' to protect engines and other mechanical devices from arbitrary levels of cold.
Atmospheric pressure is less important but much more confusing. Most of us live very close to one atmosphere (14.696 psi), which is to say, the pressure of Earth's atmosphere at sea level. There's no real point in worrying about any changes in freezing temperature as you climb a mountain; at 0.5 atmosphere, the lowest a human can survive for any length of time, the freezing points remains within a cow's thumb of 0 °C, only starting to decrease after we hit the triple point of water at 0.1° C and at a pressure of 0.006 atmospheres. At lower pressures water never becomes liquid, but prefers to remain a vapor at colder and colder temperatures as the pressure decreases, and changing from vapor directly into ice. Humans can't survive even briefly below 0.0618 atmospheres, as at that point the boiling temperature of water -- and thus blood -- approaches 98.6 degrees. Likewise, the freezing temperature starts to wiggle about in odd ways somewhere around 950 atmospheres of pressure, and at something close to 98,692 atmospheres of pressure, water is never anything but ice.
If you want to learn more about the extremes of freezing at various pressures and temperatures, you should get a visual; the phase diagram of water is more chaotic than one would expect.