Skype is almost always on when I'm online, granted my status is constantly set to 'busy'. But that's only because I don't like to see people signing in or seeing the box turn orange and flash at me from the corner when someone IMs me. I can see the notification just fine with only the small orange icon appearing. I only ever set it to 'online' when I'm expecting a call from someone, so I receive the notification and don't accidentally ignore it.
But yeah I pretty much leave Skype open most always when I'm on the computer, regardless of if I'm talking to anyone or not. It's usually fairly silent aside from a friend or two, but I still leave it open for some reason. >>;