This may sound stupid but for a long time, I was not able to remove shortcuts from the launcher in GLOME Classic. Therefore I was afraid of adding things to the launcher. I just has put Firefox, Terminal, Gedit and a green screen shot capturing app. Today, I accidentally added some other shortcuts into the launcher and faced a situation of removing them somehow. Then only I bothered to search google about it and found the solution.
The key combination Super(= Windows key) + Alt + Right-Click on the launcher icon provided me the option "Remove From Panel". Thats what exactly we wanted. Just right-clicking on a launcher icon does not provide this option. I found this solution from this forum discussion.