Have you not set a password for the MySQL root user? Try without the -p option, like this:
If you get a prompt like this:
then you're at the mysql console.
I advise you to set a password for the MySQL root user if your server is a production server or accessible from the outside. Of course if you already have applications (PHPMyAdmin or so) in place you'll have to change their configuration accordingly if you set a password.
A password for MySQL (if not set before) can be set using:
mysqladmin -u root password YOURPASSWORD