Today I got the error below :

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ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)

after typing :

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mysql -u root

I don’t know why ? but I know how to solve it.
First of all let’s disable password authentication :
Stop your MySQL daemon:

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/etc/init.d/mysql stop

or

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/etc/init.d/mysqld stop

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mysqld_safe --skip-grant-tables &

Secondly run :

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mysql -u root

Finally, In your MySQL command line prompt issue the following command:

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USE mysql;
UPDATE user SET password=PASSWORD("my_password") WHERE user="root";
FLUSH PRIVILEGES;
EXIT

Password is now reset to my_password. So just restart your MySQL server using :

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/etc/init.d/mysql restart

or

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/etc/init.d/mysqld restart

and use your new password to authenticate :

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mysql -u root -p

All that remains is to enter your password.