When attempting to export data using the accepted answer I got an error:
ERROR 1235 (42000) at line 3367: This version of MySQL doesn't yet support 'multiple triggers with the same action time and event for one table'
As mentioned above:
mysqldump --no-create-info
Will export the data but it will also export the create trigger statements. If like me your outputting database structure (which also includes triggers) with one command and then using the above command to get the data you should also use '--skip-triggers'.
So if you want JUST the data:
mysqldump --no-create-info --skip-triggers