November, 2014: If you're getting this error on MySQL 5.6.x on Mac OS X Mavericks or Yosemite and want to use MySQL with PHP locally (/tmp/mysql.sock is where PHP PDO expects to find the sock file), here is what fixed it for me:
1) Uncomment the default homebrew config file lines and edit as below
$ sudo vi /usr/local/Cellar/mysql/5.6.21/my.cnf
...
basedir = /usr/local/Cellar/mysql/5.6.21
datadir = /usr/local/var/mysql
port = 3306
server_id = <UNIQUE_NUMBER_HERE_OR_LEAVE_COMMENTED_OUT>
socket = /tmp/mysql.sock
pid-file = /usr/local/var/mysql/[BOXNAME].local.pid
....
BOXNAME is what you have in your System Prefs -> Network as the unique id for your computer on the network.
2) Set permissions on all the files in the mysql datadir. These were all owned by [my_username]. MySQL is very picky about this and refuses to create the pid file unless it (the user _mysql) owns the directory.
$ sudo chown -R _mysql:mysql /usr/local/var/mysql
3) Start MySQL using the bash helper/wrapper script:
$ sudo mysql.server start
Starting MySQL
. SUCCESS!
Hope that helps. If the above doesn't work for you, try to run the mysqld_safe binary manually in the Cellar/mysql/VERSION_/bin/ directory and check what the settings are (if it runs)
sudo /usr/local/Cellar/mysql/5.6.12/bin/mysqld_safe &
If that runs, you can
ps aux | grep mysql
and see something like
[username] 6881 0.0 2.7 3081392 454836 ?? S 8:52AM 0:00.54 /usr/local/Cellar/mysql/5.6.21/bin/mysqld --basedir=/usr/local/Cellar/mysql/5.6.21 --datadir=/usr/local/var/mysql --plugin-dir=/usr/local/Cellar/mysql/5.6.21/lib/plugin --verbose --log-error=/usr/local/var/mysql/BOXNAME.local.err --pid-file=/usr/local/var/mysql/BOXNAME.local.pid
I'm not sure why that worked for me but it shows you where I got the my.cnf config file options from. You can also use the command line options to try to troubleshoot when starting mysqld manually.
If you do run manage to run MySQL server using mysqld_safe, you may have to do this to shut it down before trying the mysql.server bash helper. Resist the urge to kill -9 [PID] because you can corrupt your data.
mysqladmin -uroot shutdown
Good luck!