ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)

Solution:

mysql> use mysql
Database changed
mysql> update user set password=old_password('mysql') where user='root' and host='localhost' ;

Query OK, 1 row affected (0.07 sec)
Rows matched: 1  Changed: 1  Warnings: 0

mysql> flush privileges;
Query OK, 0 rows affected (0.00 sec)

mysql> exit