I installed MySQL on Mac OS X Mountain Lion with homebrew install mysql, but when I tried mysql -u root I got the following error:
It's probably because MySQL is installed but not yet running.
To verify that it's running, open up Activity Monitor and under "All Processes", search and verify you see the process "mysqld".
You can start it by installing "MySQL.prefPane".
Here is the complete tutorial which helped me: http://obscuredclarity.blogspot.in/2009/08/install-mysql-on-mac-os-x.html