Why will Xcode not update? Software update always tells me Xcode 6.2 is available.  Other updates install when requested, but when I click the XCode update button it asks me for Apple ID and password.  Other items update without asking.

When I enter those, I never get an error message, and the button dims.  But nothing else ever happens.  Other things will show a progress bar and change the button text to say what is happening.

I accepted the workaround even though it's not exactly an answer to the question as asked.  But it's worth noting here that whatever caused it has been magically corrected.
As a workaround, you can download it directly from Downloads for Apple Developers if you have a (free or paid) account.

Update:  At one time the included link above would take one directly to Downloads for Apple Developers after signing in, however as time goes by things change. So once logged into your Developer account add downloads to the address in the address bar so it shows as https://developer.apple.com/downloads and then press enter.

You should then be at the Downloads for Apple Developers section as shown in the cropped clip below.