This year my husband and I went to Paris and London and spent an extended layover in Copenhagen and we had a really great set up for keeping contact with our son back home. Republic Wireless is the cell provider we use and I strongly recommend it for frequent travelers who don't want to run up roaming charges. Republic uses wifi calling and texting as a big part of their service, but you can actually change your cell service fairly often to suit what you'll use. My husband's phone is usually $10.00 a month for talk and text and wifi-only data. We switched him to a wifi only phone plan for the two weeks of our trip which cuts the monthly bill to $5.00 a month which means no data roaming and no extra charges! we used an offline gps map to help us get around and we were able to call home on wifi at our hotel or do a video chat.
In the event you get a call or text when you are not connected to wifi, the message is stored until the phone connects. No messages lost as can happen when roaming with a typical cell plan.
Some places specifically block wifi calling on their wireless network, in that case google hangouts/skype/facetime worked just fine.
If you are a Republic Wireless user or you want to find a low cost cell carrier that works great internationally, we found no problem using our phones in the 3 countries we visited. My sister was shocked when I called her from London, and it was absolutely free!