I have previously reported this as a potential Logitech Webcam C270 issue, but it is now clear that it is actually a conflict between Skype for Desktop 22.214.171.124 and the AMD display driver 126.96.36.199, when running Windows 10 build 10074. (I have an AMD Radeon HD 7750 graphics card).
If I start Skype for Windows Desktop and do "Tools->Options->Video Settings" , I get a popup message about the AMD display driver failing to respond. In the System event log I see the message "Display driver amdkmdap stopped responding and has successfully recovered". Skype never manages to display the webcam preview.
From the Skype forum there are numerous reports of various versions of Skype crashing the AMD display driver on both Windows 8 and 7.