6 or 7 years ago it did, today it’s mostly used by the tech illiterate who don’t know who the developers are or what it does to their computers while it’s running.
NINJA Clarification:
Skype is made by the same developers as Kazaa and while it’s running your PC joins their peer-to-peer network and is used as a node to forward and route calls and user location information. Skype actually owns very few servers as most of the network and call processing load is offloaded to the skype user network.