[mysql] Can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)

I hope this helps somebody. I was getting the same error, but seemingly for a much different reason than other people.

I have 2 CentOS machines.

I copied my.cnf to the new machine, not realizing that I had upgraded the old machine to MySQL 5.6, and the new machine had 5.5 installed. When I commented out the 5.6-only directives, MySQL started as expected. (and now I am running the upgrade so I can apply the massively useful innodb_buffer_pool_dump_at_shutdown and innodb_buffer_pool_load_at_startup directives)

I would suggest trying a bare minimum my.cnf. If MySQL starts up, then you've found the source of your problem.