If you don't remember the password you set for root and need to reset it, follow these steps:

Stop the mysqld server, this varies per install
Run the server in safe mode with privilege bypass
sudo mysqld_safe --skip-grant-tables;

In a new window connect to the database, set a new password and flush the permissions & quit:
mysql -u root

For MySQL older than MySQL 5.7 use:

UPDATE mysql.user SET Password=PASSWORD('your-password') WHERE User='root';

For MySQL 5.7+ use:

USE mysql;

UPDATE mysql.user SET authentication_string=PASSWORD("your-password") WHERE User='root';

Refresh and quit:

FLUSH PRIVILEGES;

\q

mysql> UPDATE mysql.user SET Password=PASSWORD('your_new_password')
       WHERE User='root';
ERROR 1820 (HY000): You must reset your password using ALTER USER statement before executing this statement.

mysql> SET PASSWORD = PASSWORD('your_new_password');
Query OK, 0 rows affected, 1 warning (0.01 sec)

Stop the safe mode server and start your regular server back. The new password should work now. Worked like a charm for me :)