The kind of alcohol that people can drink is called ethanol and it has a freezing point of -114 degrees celcius (-114 °C). However, there are many other kinds of alcohol (such as methanol, rubbing alcohol or isopropanol, butanol, and many others) and each one has a different freezing point.
Water freezes at 0 °C and the coldest most home model freezers will go down to -18 °C. That is why alcoholic beverages won't freeze in your home freezer. However, most alcoholic beverage are not pure ethanol, but instead a mixture of water and ethanol. The freezing point of the mixture depends on how much of each component is in it. For instance, something with only 1% ethanol will freeze just a little below 0 °C, whereas something with 95% ethanol will freeze pretty close to -114 °C. How much ethanol is in a particular alcoholic beverage is listed on the bottle, either as a percentage or as a "proof" which is just 2 times the percentage (100 proof = 50% ethanol).