I am assuming you want to stop notifications from ASC. Frank Caggiano's document is very easy to follow …
And you can't close your account either! What you have to do is just stop using it.
as for emails normally you have sub-scribe / unsubscribe option....
you can also report as spam ........ http://support.apple.com/kb/ts4019
you can also forward them to trash....http://macs.about.com/od/usingyourmac/qt/mailrules.htm
what type of emails ????