Source: http://lifehacker.com/5566346/vodburner-records-and-edits-skype-video-chats
Windows only: Vodburner is an application that will record your Skype video chats and conferences, with the capability to edit the recorded video. The program saves those important business teleconferences or personal conversations with friends for future reference.
If the other party of the Skype conversation does not have Vodburner installed, Vodburner will watermark the video when you record the video chat (unless you pay to upgrade the software). If both parties have it installed, Vodburner does not leave a watermark. As a courtesy, upon each call, Vodburner will ask if you want to alert the other person that they are being recorded.
Vodburner also has limited and basic video editing features, including basic transitions, so if that's all you want to do, there's no need to go into a separate video editing program. Either way, these six popular video-editing applications can probably help if you are looking for more editing functionality. Vodburner is a free download for Windows only.