See this article from Skype FAQ for the solution(s): How do I remove Skype from the Taskbar?
When you are signed in to Skype, the Skype logo is displayed in the
Windows taskbar. You can also see your Skype status icon displayed in
the system tray at the bottom of your screen.
If you close the Skype window, the Skype logo and status icon still
appear in both the Windows taskbar and the system tray.
To remove Skype from both the Windows taskbar and the system tray,
right click the status icon in the system tray and select Quit. This
completely closes the application and signs you out, which means you
will no longer receive instant messages or calls through Skype.
You can change your settings so that Skype is removed from the Windows
taskbar when you close the application window by clicking X. This
doesn’t sign you out, so you can still receive calls and instant
messages while Skype runs in the background. You will still receive
notifications for any IMs you receive in the system tray.
To do this:
- Sign in to Skype.
- Select Tools > Options....
- Select Advanced > Advanced Settings.
- Uncheck the box next to Keep Skype in the taskbar while I’m signed in.
- Click Save.
Now every time you close the application window, Skype should no longer
display in the Windows taskbar. If it does, then you may have to change
the program properties. To do this:
- Click the Start menu.
- On Windows 7/Vista: Select Computer.
On Windows XP: Select My Computer.
- Open Local Disk (C:)
- On Windows 7/Vista: Select Program Files(x86).
On Windows XP: Select Program Files
- Locate and open the folder named Skype.
- Open Phone.
- Right-click Skype.exe and select Properties.
- In the Compatibility tab, uncheck the box next to Run this program in compatibility mode for: