I have no Windows recommendations since I had moved off Windows to Mac back in 2005, and since Dec 2014 I am now on Linux (for everything except music recording & production), but I do have a few ideas that might work for you based upon the results I just found for Linux.
For Linux, lots of the answers to similar questions on other forums seem to be focused upon using one of the screen recording or 'screencast' apps for Linux, such as Kazam or Vokoscreen, both of which let you define either the entire screen, a specific window (or program), or a specific area to record along with options for the sound from your mic and speaker, into a variety of different formats, with the default being an h.264 MP4 video.
SO, my thinking is that if there is not a free Windows app that lets you have direct integration with Skype itself, maybe a 'screen recording/capture' app would work for you in Windows. I am not sure if they are still around, but I remember that SnagIt and Camtasia were popular back in the day.
Sorry I could not offer more help for Windows. The Skype forums have many discussions on this topic right now, but I do not see one app that is loved more than others, or that crashes less than others based upon my initial scanning of their forum threads.
For myself, I plan to test Kazam and Vokoscreen (for capturing a Skype video call), which I've already got installed, and if you are on a Debian-based Linux distro (like Ubuntu), they are both in the default software repositories, and can easily be added to your system with a simple 'sudo apt-get install kazam && vokoscreen' from a terminal prompt (of if you want a GUI to do it, you can use Synaptic).
Slightly off topic -- For anyone who might be interested, when I built this Linux computer back in Dec 2014, I did a lot of research for HD Linux webcams and ended up getting the Logitech C920C model, which is a full 1080p camera with stereo noise canceling mics, and does h.264 compression in hardware on the camera before the video stream hits your USB port, which lowers the required bandwidth of the video that has to be fed into your USB port (due to the stream already being compressed). It is also one of the FEW cameras that work on Mac and Linux as well as Windows (i.e., class-compliant USB and NOT needing any funky drivers)
Both the video and audio quality are impressive and for testing I used the app GUCView, and CheeseCam to make a few test videos, and VLC (VideoLan Client) can ALSO capture video from this camera.
I've also tested the video recording function of this Logitech camera on my late-2012 i7 Quad-core Mac Mini (which I ONLY use for music production) in both Quicktime and iMovie and it works really great on Mac OSX 10.9 Maverix as well, without any drivers.
Hopefully, at least this info might help someone looking for a webcam to use across different operating systems.