There are so many options to connect when you travel nowadays besides just using your phone as a..ahem...phone.
The ones I have found are
Out of all of these, WhatsApp has seemed the most common in Latin America, right now in Peru in some areas the Police number on their vehicles shows whatsapp xxxxxxxxx
In Russia again WhatsApp was very popular for not only calling but sharing photos and videos
One downfall I had with WhatsApp is it needs a working phone number to initially be set up, my phone got wet and I had to do a hard reset in Colombia, the US phone number I was using failed to reconnect the app so it was lost...thats just as an FYI.
What do you use internationally and have had the most success with connectivity?