I have a problem, It's been months since I used MySQL and (I believe) I had set it up with a root password.  Now I can't log on to MySQL as root MySQL user and create a new user or manage an existing user (I can log onto server)...

Familiar situation. :)

Do so:

 service mysql stop

wait until MySQL shuts down. Then run

mysqld_safe --skip-grant-tables &

then you will be able to login as root with no password.

mysql -uroot mysql 

In MySQL command line prompt issue the following command:

UPDATE user SET password=PASSWORD("abcd") WHERE user="root"; 

FLUSH PRIVILEGES;

At this time your root password is reset to "abcd" and MySQL will now
know the privileges and you'll be able to login with your new password:
 

mysql -uroot -pabcd mysql