Backup

mysqldump --routines -u root -p --databases db1 db2 db3 | gzip > /var/www/backups/mysql/databases.sql.gz # multiple db using gzip
mysqldump --routines -u root -p --databases db1 db2 db3 | bzip2 > /var/www/backups/mysql/databases.sql.bz2 # multiple db using bz2

mysqldump --routines -u root -p db1 | gzip > /var/www/backups/mysql/db1.sql.bz2 # single db using gzip
mysqldump --routines -u root -p db1 | bzip2 > /var/www/backups/mysql/db1.sql.bz2 # single db using bz2


Restore

bunzip2 < db1.sql.bz2 | mysql -u root -p db1
zcat db1.sql.gz | mysql -u root -p db1


Same goes for multiple DBs just add one or more DB to restore at the end of the command, or leave blank to restore all.