Apple's system for iMessage and FaceTime is designed so that Apple creates private keys and can't access them later or spoof new ones. The same is true for all systems that rely on the Signal protocol developed by Open Whisper Systems, which includes the Whatsapp messaging system's software.
Adding to concerns, Microsoft eliminated peer-based Skype supernodes in 2012 and moved all supernodes to the cloud. At the time, some speculated that was to allow easier "wiretapping," although that ability already existed. Shifting to the cloud makes it easier still, though not much more. Skype will also support a Web-based app, which by its nature will have less ability to provide strong end-to-end encryption.
Cloud cuckoo land
Microsoft put out a statement about the latest move: "The changes to Skype's architecture will not impact our current privacy statement. We are committed to delivering a secure experience for our users and Skype software applies highest industry standard encryption to all Skype audio and video calls. It is an important part of our security strategy now and as we make the transition over to a cloud infrastructure."
This answers zero questions about what that secure experience is and how it's implemented. With options like iMessage for Apple ecosystem users, WhatsApp for nearly every platform, and extremely strongly protected additional offerings like Signal from Open Whisper and Silent Circle's hardware and apps, there's no reason to settle.
If you want to have the most robust and most protected communications, regardless of the reason, Skype isn't it. The move to the cloud makes it worse at privacy than it was before, but without a full, independent, and released report on the apps, algorithm, and infrastructure, we can only assume they don't meet the high bar set by so many other apps and systems.
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