Disable SubmitDiagInfo
Going to System Preferences &gt; Security &amp; Privacy &gt; Privacy &gt; Diagnostics &amp; Usage and unchecking Send diagnostic &amp; usage data to Apple did not work for me. I still get the Little Snitch dialog asking for permission to connect to radarsubmissions.apple.com.

It seems the connection attempt is triggered by a launchd job located at /System/Library/LaunchDaemons/com.apple.DiagnosticReportCleanUp.plist. On Mountain Lion 10.8.4, it's set up to run every day at 11 am. If I clear the Little Snitch rules for the SubmitDiagInfo process and run the following command to start the launchd job sudo launchctl start com.apple.DiagnosticReportCleanUp, the Little Snitch connection dialog pops up.

This seems to be a bug as the DiagnosticReportCleanUp job is not respecting the Privacy setting in System Preferences. I've denied the connection attempt Forever in Little Snitch for now. Hopefully, this gets fixed in OS X 10.9 Mavericks.