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You can accomplish this using the mysqldump command-line function.
For example:
If it’s an entire DB, then:
$ mysqldump -u [uname] -p db_name > db_backup.sql
If it’s all DBs, then:
$ mysqldump -u [uname] -p --all-databases > all_db_backup.sql
If it’s specific tables within a DB, then:
$ mysqldump -u [uname] -p db_name table1 table2 > table_backup.sql
You can even go as far as auto-compressing the output using gzip (if your DB is very big):
$ mysqldump -u [uname] -p db_name | gzip > db_backup.sql.gz
If you want to do this remotely and you have the access to the server in question, then the following would work (presuming the MySQL server is on port 3306):
$ mysqldump -P 3306 -h [ip_address] -u [uname] -p db_name > db_backup.sql
It should drop the .sql file in the folder you run the command-line from.
EDIT: Updated to avoid inclusion of passwords in CLI commands, use the -p option without the password. It will prompt you for it and not record it.
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