Same thing happened to me last night at about 02:30 GMT while I was fast asleep and my computer was off.
Facetime made a few phone calls on its own, setting off panic buttons all around the world to random people on my address book.
Following many emails and worried phone calls this morning, I launched Facetime and there were no records of any 'recent calls'.
I only have Facetime on my laptop, not on my phone but it was so weird I thought I was losing my mind. When I tried to delete the application following a friend's advice, I got an error message saying that it cannot be deleted because the application is in use, even though it wasn't. I really had to struggle to get rid off it, restarting a few times.
Can anyone explain what is going on?