ShareMeNot does not share any user data with us or with anyone else.
If you have the "Automatically add exceptions" setting enabled in Firefox (enabled by default), ShareMeNot will keep track of the list of websites on which you have clicked buttons supported by ShareMeNot. You can view and edit this list on ShareMeNot’s preferences page (Tools > ShareMeNot > Manage Options...), and this list is never sent anywhere outside of your browser.
ShareMeNot is configured to automatically update via Firefox’s and Chrome's update mechanisms. If you do not wish for ShareMeNot to update automatically, you can disable this feature from the Firefox add-on menu (Tools > Add-ons) or from Chrome's extension menu (Wrench button > Tools > Extensions). There you may also disable or uninstall ShareMeNot.