Do you know you can have two instances of skype opened with the same account in different computers?
I discoverd it using the ipod touch client and at the same time my laptop was running another instance…nice feature…or not?
Both the skype instances will show your chats: if someone is in front of the other pc he/she well be able to read your chats.
So? better to add a password on the pc (both, screensaver and login) to avoid risks.
Microsoft messenger behaviour: it closes the connection on the pc with the older session.