To prevent the problem from occurring, you must perform a graceful shutdown of the server from the command line rather than powering off the server.
# shutdown -h now
This will stop the running services before powering down the machine.
Based on Centos, an additional method for getting it back up again when you run into this problem is to move mysql.sock:
# mv /var/lib/mysql/mysql.sock /var/lib/mysql/mysql.sock.bak
# service mysqld start
Restarting the service creates a new entry called mqsql.sock