I found out how to do it, on a Mac. All you do is click their name once in the contacts list (their name should now be highlighted in blue), then press "delete" on your keyboard (above "enter"). A box will appear and ask you if you are "sure you want to remove _______ from your contact list?" Click "Remove" and voila, they're gone.
I have tried all the methods suggested, but none work. When I hit the delete I just get a plonk sound. Surely this is something the operators of Skype should have resolved, as it is clear there are many users that have the same problem.. Any ideas how to get hold of Skype to get an answer? I have downloaded the latest version - still cannot delete contacts!!
Thanks for your advice - but it didn't work for me on my Mac - I don't have a 'right click' system and when I highlighted the name, the option to DELETE in the EDIT menu is greyed out. Pressing the delete key doesn't work either. What a rubbish system! Aren't there any competitors out there? Everything went downhill after I downliaded an upgrade....