According to the Christian Bible Reference Site, the word sin is mentioned over 400 times in the Bible. Depending on the version of the Bible, the count is slightly different but is never less than 400.
Sin is mentioned so many times because the Bible considers it a very serious problem. Many different types of sin are mentioned, so the total count that any type of sin is mentioned would be even higher. The Bible states that everyone has sinned (Romans 3:23), that the punishment is death (Romans 6:23) and that all sin can be forgiven by trusting in Jesus Christ (Romans 10:9).