Extracting a remote MySQL Database without MyODBC?

MySQLDump has a -h parameter to connect to a remote host.

First try the mysql client application:

mysql -h your.server.com -uYourUser -pYourPass

If that works, use the same format for MySQLDump

mysqldump -h your.server.com -uYourUser -pYourPass --all-databases

Edit for ajreal:

By default, mysqld (the MySQL server) will run on 3306, and mysql (the client application) will connect using that port. However, if you changed your configuration, update your command accordingly. For example for port 3307, use

mysql -h your.server.com -P 3307 -uYourUser -pYourPass

Check your MySQL configfile to see how you can connect to your MySQL server.