I just tested this myself and it seems to work well. @debfx, what can I do to help get this in the next release?

Working fine, but how do you actually close the application if you want it ?
Right click on tray -> Quit doesn't work, same happens when selecting Quit from the Menu.

Send the process a SIGTERM or SIGKILL signal; that's the only way to close it with this change and the feature enabled.

Well yeah, anyway I added something to quit with a middle click on tray icon and it works.

src/gui/MainWindow.cpp

void MainWindow::trayIconTriggered(QSystemTrayIcon::ActivationReason reason)
 {
     if (reason == QSystemTrayIcon::Trigger) {
         toggleWindow();
    }
+    if (reason == QSystemTrayIcon::MiddleClick) {
+         reallyQuit();
+     }
 }



+void MainWindow::reallyQuit()
+{
+    bool accept = saveLastDatabases();
+
+    if (accept) {
+        saveWindowInformation();
+        QApplication::quit();
+    }
+    else {
+      QApplication::quit();
+    }
+}
+
 void MainWindow::lockDatabasesAfterInactivity()
 {

src/gui/MainWindow.h

     void toggleWindow();
+    void reallyQuit();
     void lockDatabasesAfterInactivity();

I think choosing the "Quit" option from the tray context-menu should actually kill the program; when would you ever want to use that (remember, from the tray...) to minimize the program? If someone did want the minimize action, it'd probably be better to add a "Minimize" entry.

Oh, hah: clicking the tray icon already does this "minimize" behavior. I think that basically settles the point then: the Quit option from the tray should reallyQuit. What do you think?

Yeah exactly, that's how it should be.
I just didn't know how to do that (quit from the tray -> reallyQuit) so I added middle click thingy, which works from me atm until someone smarter figure out the real Quit from the tray :)

I'll try and clean this up and see if I can get it in. @plafue, are you still wanting to see this included too?

I figured out actually how to add an option to the tray and it works.
Now probably good idea would be to remove Quit from the tray menu, not sure though what to do with the Quit option from Main Menu. Middle click on tray is also not needed now.
Here's the addition to the tray menu, needs reallyQuit() from earlier.
src/gui/MainWindow.cpp

             QAction* actionToggle = new QAction(tr("Toggle window"), menu);
             menu->addAction(actionToggle);
+       QAction* actionToggle = new QAction(tr("Really Quit"), menu);
+            menu->addAction(actionReallyQuit); 

             menu->addAction(m_ui->actionQuit);

             connect(m_trayIcon, SIGNAL(activated(QSystemTrayIcon::ActivationReason)),
                     SLOT(trayIconTriggered(QSystemTrayIcon::ActivationReason)));
             connect(actionToggle, SIGNAL(triggered()), SLOT(toggleWindow()));
+       connect(actionReallyQuit, SIGNAL(triggered()), SLOT(reallyQuit()));

             m_trayIcon->setContextMenu(menu);
             m_trayIcon->show();