I've noticed that Skype isn't ringing after I upgraded Skype after upgrading to Windows 7. In other words there's no ringing sound on incoming calls. To get skype to ring again, just follow the instructions below.

Skype No Ring - Solution

1. Open your Skype program.
2. Click 'Tools'.
3. Click 'Options...'.
4. Select the 'Audio Settings' icon.
   
5. Set the 'Ringing' drop-down option to 'Ring on all devices'.
   
6. Click the 'Save' button.