In case this has passed you by, WordPress 3.7 introduced Automatic Background Updates. The major core releases will not be automatic but security and minor releases will be. If like me, you would prefer to control, even the minor updates yourself, then I have found a plugin that gives you back the control.
Another way to get control back is outlined here at WordPress.org, “configuring automatic background updates” but this method involves adding a line of code to your wp-config which you would need to do via FTP.
I want to point out that automatic background updates “should” be very stable and not cause problems to the majority of sites but inevitably, there will be some sites that could potentially have problems, e.g. Sites that still have old themes or plugins.
This is the plugin I found, called “update control” and you simply install in the usual way, then go to your Settings/General area of your dashboard and configure how you want the plugin to behave, there is a box to completely disable any automatic updates to WordPress.