Yes, Volatility Can Be Zero
Volatility can reach values from zero (inclusive) to positive infinite.
When Is Volatility Zero?
Being the bottom of the value range, zero is obviously a very special case of volatility.
Volatility is zero if there are no changes in the price (the price is constant).
For example, if there was a stock and its price would stay at 20 dollars and never change, then its volatility would equal zero.
Of course, in reality there are not many assets with constant prices. And for those that have a constant price, it makes little sense to calculate or analyze volatility, because it is obvious that it is zero.
How Is Volatility Calculated?
The range of possible values is a direct result of the way volatility is calculated.
Historical volatility is calculated as the standard deviation of logarithmic returns. Its value range is the same as the possible value range of standard deviation (from zero to positive infinite).
If you are not familiar with volatility calculation or with the concept of standard deviation, see:
You can easily calculate volatility in Excel (using a combination of functions, including especially the STDEV.S function). Here you can download the Historical Volatility Excel Calculator and Guide.