Recently one of my servers was complaining about having /var partition full! Found that the blame could be attributed to a los of files mysql-bin.000001 in /var/log/mysql/, each file was about 80MB. MySQL stores update queries for all databases, you can take a look with:

mysqlbinlogs mysql-bin.000001

Also found in the documentation that mysql can take care of purging those files every period of time automatically adding the following to /etc/mysql/my.cnf under [mysqld] section: