If your MySQL data directory has many files such as:
mysql-bin.000001
mysql-bin.000002
etc..
that means that the [mysqld] option:
log-bin=mysql-bin
is enabled in your /etc/my.cnf (or in the startup script).The solution to prevent those files from being created is to comment out the log-bin option from the my.cnf.
The internal default is "OFF", hence removing it will disable it.
You can delete your mysql-bin.0* files after mysqld has been restarted.