How to configure global charset on MySQL
You need to incorporate the following into your my.cnf file

[client]
default-character-set=utf8

[mysql]
default-character-set=utf8


[mysqld]
default-character-set = utf8    
collation-server = utf8_general_ci
init-connect='SET NAMES utf8'
character-set-server = utf8


You can find more information on the following manual pages


http://dev.mysql.com/doc/refman/5.6/en/charset-configuration.html
http://dev.mysql.com/doc/refman/5.6/en/server-system-variables.html#sysvar_character_set_system 
http://dev.mysql.com/doc/refman/5.6/en/server-system-variables.html#sysvar_character_set_server


In response to Mark's answer, if you need to convert existing tables/databases to the correct character set you will need a suitable ALTER query. Something similar to the below:

ALTER TABLE `table` CONVERT TO CHARACTER SET utf8 COLLATE utf8_unicode_ci;


Alternatively there's a great PHP script here which does it for you.