The Skype "Heartbeat" page notes:
UPDATED 14:02 GMT: Some of you may be having problems logging into Skype. Our engineering team has determined that it’s a software issue. We expect this to be resolved within 12 to 24 hours. Meanwhile, you can simply leave your Skype client running and as soon as the issue is resolved, you will be logged in. We apologize for the inconvenience.
Additionally, downloads of Skype have been temporarily disabled. We will make downloads available again as quickly as possible.