As of yesterday my N9 no longer logs into Skype. It prompts me to enter my password, which I do, but it says wrong password (the password is 100% certainly correct).

There have been some recent updates to Skype in general, which I believe has forced some people with older clients to upgrade. So is Skype on N9 no longer supported?

That will rather quickly relegate the N9 to 'backup phone' status, and bring back the iPhone as primary.