I am abroad every week and found an easy answer to this one. I usually have wi-fi in the airport lounge and hotel, and like you use skype etc.

Get an app called Hullomail and sign up to it. It asks for an email address.
http://hullomail.com/us/index.html

At the airport as I depart I put divert voicemail calls to Hullomail, and when I get back I turn it off. What it does is convert your voicemail to a .wav file and emails it to you as an attachment. You pick it up as an email on the wifi.

It is a free app, so you can sign up for it and try it at home before you depart so you can see how it goes. At that price you cant really go wrong!