Suspicious data transfer

I often notice via the Local Area Connection icon that my computer is communicating via the Internet with some unknown site (that is, it reports bytes sent and received).  How can I identify this connection?  That is, how can I identity who my computer is communicating with?  If it is a Norton Update, I suggest that Norton add an indicator to its Norton Antivirus Online status window indicating that it is currently online.  Otherwise, is there a program that can tell me who my computer is communicating with.  A deep Norton scan of my computer reveals not viruses other than an occasional cookie.  I end up disabling the Internet connection to stop the communication.  Of course, this means I have to take the extra step to re-enable the connection.