When you downloaded Skype, it was placed into quarantine. (Specifically, an extended attribute named com.apple.quarantine was added to it.) Well, actually it was added the .zip or .dmg file it came to you as, but was propagated to the actual application when you unzipped or opened the .dmg.
To make the message go away, the quarantine flag has to be removed. The easiest way to do that is to select the app in Finder (not in the Dock, not in the Launchpad) and right-click or control-click on it to get the contextual menu. Select "Open" from the contextual menu. You'll have to authenticate as an admin, but once you've done that you won't ever see the dialog again for that app.
OK I tried that, and now it opens without interrogating me, many thanks...
I did not have to authenticate as an Admin - it just stopped asking me.
FWIW I'm on 10.6.8 - this might help someone else?
