First of all, why would you remove it? Your databases will be open to any user that's able to connect to your server by using root as login without providing a password. That's a pretty big security risk unless you have your server secured in other ways and you're the only user that has access to it.
One possible way:
mysql -u root -p [login using your password]
mysql> use mysql;
mysql> update user set password=PASSWORD("") where user='root';
mysql> flush privileges;