I'm a journalist. (Kind of.) I have to record calls a lot, to supplement my notes. When I make a call over Skype, I use Ecamm Call Recorder, a simple but full-featured Mac-only Skype extension.
"Hi, who just joined?"
The compact Call Recorder interface
Call Recorder (the app name equivalent of "The Band") automatically opens when Skype opens, which is crucial, because otherwise I'd forget to start recording. Even better, you can tell Call Recorder to start recording every time you make a call. (To avoid file clutter, the app can discard short calls.)
It's useful for recording important conversations, interviews, or podcasts. It costs a hefty $US39.95 ($53), but if you frequently record Skype conversations, it's worth it. The licence works on multiple devices, and includes all future app updates. Call Recorder is also available for FaceTime, also for $53.
Call Recorder's settings menu integrates into the rest of the Skype settings
Call Recorder doesn't alert anyone on the call about its presence, so you can record without the other person noticing. But it's polite and ethical (not to mention a legal obligation) to let them know. If you plan to secretly record a call, check local laws so you know what you're getting into.
Recording is one of those basic features that should come with the original app; maybe Skype just doesn't want people to worry they're being recorded. As if anyone still expects privacy these days.