What permissions do you need to take a mysql database backup via SSH?
Depending on the options you use with the dump you may need more (or less). The one you definitely need is SELECT. 


If you use triggers you need TRIGGER
If you use views you need SHOW VIEW 
If you don't use --single-transaction in the dump you will need LOCK TABLES 


For more info on the subject you can go to: http://dev.mysql.com/doc/refman/5.5/en/mysqldump.html