In the system tray click on the up arrow >> Click Customize...
Set Skype to Show icon and notifications.
I have Vista and my screens do not look like this. I am offered the Skype icon only in the "PAST ITEMS" area of my customize notification icons screen. Selecting "show" in the behavior column did not bring back my icon in the system tray (notification icons). I was signed into Skype and the application was running when I did this.
Please reinstall skype with this link