When emails are sent via the application, how come I never receive the emails?

The most likely cause of this problem is that the SMTP on the web server hosting the application is not configured correctly. Read the SpiraTeam Administration Guide which includes an appendix containing detailed instructions for configuring SpiraTest, SpiraPlan, or SpiraTeam to send email notifications.

For KronoDesk, please read the KronoDesk Administration Guide which includes an appendix containing detailed instructions for configuring KronoDesk to send email notifications.

When sending emails using an email server that requires SSL/TLS (e.g. Gmail) I keep getting 'Command not implemented. The server response was: Command not Supported' errors

This has been confirmed as a bug in the .NET Framework by Microsoft that occurs because the remote SMTP server does not support the SMTP extended Hello (EHLO) command and .NET is not able to handle the return code. This has been fixed in a hotfix which can be downloaded from http://support.microsoft.com/kb/913616.