This is a tricky one, I have the following output:
mysqldump: Got error: 1045: Access denied for user \'root\'@\'localhost\' (using password: YES) when tr
mysqldump -u (user) -p(passwd) -h (host_or_IP) database_to_backup > backup_file.sql
example:
mysqldump -u god -pheaven -h 10.0.10.10 accounting > accounting_20141209.sql
this would create sql backup file for the accounting database on server 10.0.10.10. Sometimes your error is seen when localhost is not in config. Designating ip of server may help.