This is actually a very tricky question.
Scientists who study snowflake patterns have found that the popular saying isn't quite true - there are many snowflakes that look exactly the same. This is because there are only a certain number of patterns snowflakes make, and eventually these start to repeat themselves.
However, there's more to the story than that! Everything is made up of tiny particles called atoms. If you took a really, really powerful microscope, and looked at how the atoms were arranged in each snowflake, it would be virtually impossible to find any two snowflakes that were the same.
So although it's not quite true that each snowflake is unique (at least to the naked eye), if you go down to a small enough level, each snowflake is still different than any other!