You can recover MySQL database password with following five easy steps.

1. Stop the MySQL server process.
2. Start the MySQL (mysqld) server/daemon process with the --skip-grant-tables option so that it will not prompt for password
3. Connect to mysql server as the root user
4. Setup new root password
5. Exit and restart MySQL server

Here are commands you need to type for each step (login as the root user):

Step # 1 : Stop mysql service

/etc/init.d/mysqld stop

Output:

Stopping MySQL database server: mysqld.

Step # 2: Start to MySQL server without password:

mysqld_safe --skip-grant-tables &

Output:

[1] 5988
Starting mysqld daemon with databases from /var/lib/mysql
mysqld_safe[6025]: started

Step # 3: Connect to mysql server using mysql client:

mysql -u root

Output:

Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 1 to server version: 4.1.15-Debian_1-log

Type 'help;' or '\h' for help. Type '\c' to clear the buffer.

mysql>

Step # 4: Setup new MySQL root user password

mysql> use mysql;
mysql> update user set password=PASSWORD("NEW-ROOT-PASSWORD") where User='root';
mysql> flush privileges;
mysql> quit

Step # 5: Stop MySQL Server:

/etc/init.d/mysql stop

Output:

Stopping MySQL database server: mysqld
STOPPING server from pid file /var/run/mysqld/mysqld.pid
mysqld_safe[6186]: ended

[1]+  Done                    mysqld_safe --skip-grant-tables

Step # 6: Start MySQL server and test it

/etc/init.d/mysql start
mysql -u root -p