Note: For MySQL 5.7+, please see the [answer from Lahiru] to this question. That contains more current information.
For MySQL < 5.7:
The default root password is blank (i.e., an empty string), not root. So you can just log in as:
mysql -u root
You should obviously change your root password after installation:
mysqladmin -u root password [newpassword]
In most cases you should also set up individual user accounts before working extensively with the database as well.