Here is what I use to make a backup library of MySQL daily that will keep backups for 30 days.
mysql_backup.sh
#!/bin/sh
#
# Daily MySQL Backup
#
BACKUPDIR=/backup/mysql
BACKUPFILE=db-backup_`date +"%Y-%m-%d-%H"`.sql.gz
BACKUPDAYS=30
DBHOST=localhost
DBNAME="mysql db1 db2"
DBUSER=dbuser
DBPASS=dbpass
MYSQLDUMP=`which mysqldump`
GZIP=`which gzip`
FIND=`which find`
# latest daily backup
${MYSQLDUMP} --flush-logs -h${DBHOST} -u${DBUSER} -p${DBPASS} --databases ${DBNAME} | ${GZIP} -9 > ${BACKUPDIR}/${BACKUPFILE}
# uncomment below if you are running a master/slave and you want to create a new binlog
#${MYSQLDUMP} --flush-logs --master-data -h${DBHOST} -u${DBUSER} -p${DBPASS} --databases ${DBNAME} | ${GZIP} -9 > ${BACKUPDIR}/${BACKUPFILE}
# delete old backups
${FIND} ${BACKUPDIR} -mtime +${BACKUPDAYS} -delete -print