MySQL databases are located on /var/lib/mysql. If you create a partition for /var and if it is not big enough to hold your databases MySQL will stop working. Below is the easy way to fix it:

Assume you have /home partition which is far more bigger than /var, we can move to /home/mysql

service mysql stop
cd /var/lib
mv mysql /home
ln -s /home/mysql .
chown -R mysql.mysql mysql
service mysql start