Do not use Skype for discussing personal or sensitive matters. Consider replacing Skype with software and services that support "end-to-end encryption," which involves encrypting messages and voice traffic locally before sending them on to others. Jitsi is a video, voice and text chat application that includes end-to-end encryption by way of the off-the-record (OTR) and zRTP protocols. Pidgin, a text chat application, also supports OTR.
Find more information on OTR.