Following roughly a week of user reports on the Skype support forums, Microsoft has confirmed (in an awkward way) that Skype will no longer support users running OS X version 10.5.8 or older. Skype's official response to user complains explained that Skype still works on OS X 10.6 and higher, and encouraged all of its users to stay up-to-date with the latest version of OS X and Skype.
Users are finding different work arounds that include downloading previous versions of the app and using apps to restrict Skype's access to the internet to stop automatic updates, but nothing really beats having proper support from Skype.
Consider for a moment that Mavericks runs on MacBook Pros and iMacs from 2007 onward, and MacBook Airs from 2008 and onward, though — with Snow Leopard (10.6) support going further back than that. You have to have a pretty old machine to be "stuck" on OS X 10.5.8 and unable to run Skype. That said, it definitely doesn't hurt any less if you're someone who relies on Skype and a Leopard machine.