How Do I Remove Duplicate Apps From Launchpad?
First make sure you don't really have three copies of the Application. You can use spotlight to clean out any duplicates and keep one copy of the application mounted.

Once that is resolved, you can delete the duplicates from Launchpad one by one; if they all go, just reinstall Skype.  

You can also force Launchpad to recreate its database, if it is corrupt, or just to refresh the apps alphabetically by using this hack:


run Terminal
execute sudo rm ~/Library/Application\ Support/Dock/*.db
execute sudo killall Dock to restart Dock and Launchpad


Just be aware that you will use any user-defined grouping/sorting etc. this way.

Another wonderful high-level (and safe with undos and backups) GUI solution is Launchpad control, which is a system preference panel.