All the functionality of simpleContact is within the application files and installed on your server. There is no dependency on externally hosted services. Only one call is made to my website, when you log into the admin. It reads an XML file to check whether a new version is available (a message appears on the page).
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simpleContact Lite
This file is read: http://www.simplecontactform.com/lite/version.xml
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simpleContact Pro
This file is read: http://www.simplecontactform.com/pro/version.xml
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Update: Versions of Lite prior to 1.21 and Pro prior to 2.01 refer to version files on alex-hardy.co.uk. Those URLs are now 301 (permanently) redirected to those above.
I take my user's privacy very seriously. Nothing is logged on my website and I have written a hack that instructs you how to disable the version check if you wish.