Do I need to turn off answering machine before Shabbos? I'm talking about where the message comes to your machine, not to your provider like by mobiles. Would this be the same by having a phone turned on and someone calling, or receiving an SMS?
Rabbi Frand mentioned this case in one of his weekly shiurim. He said that someone in the United States can call Eretz Yisrael on Erev Shabbos and leave a message on the machine (or send a FAX) as long as the person in Eretz Yisrael does not read the FAX or listen to the message. Many people turn the answering machine off in order not to accidentally hear the message. However, this is not required. It is better to just set it up not to play the message as it is being received (or turn down the volume) before Shabbos.
After shabbos, one listens to the message in the same way that one opens the snail mail or logs on to the computer to get the email that came in over shabbos.