We decided it would be a good idea to have a cell phone that works during our trip, and I took on the responsibilty of figuring it out. Kate's phone is a simple Verizon phone. We didn't even consider carrying this because it doesn't support web browsing, GPS/maps, and isn't GSM (the phone technology used throughout Europe). My phone is an unlocked, Android, GSM phone with T-Mobile. At home I use a cheap monthly plan that won't do international roaming (even for a fee).
After a bit of reading, along with suggestions from a friend who had also traveled in Europe, I decided to get a pay-as-you-go SIM card in Europe. Acquiring it was one of the first things we did in Ireland. No contract. In fact, aside from the intentionally unclear pricing, it was as easy as buying fast food and only a bit more expensive. This ease of purchase is not true for all countries. Some require a local address and more customer details.
After swapping my T-Mobile card for the Irish one I had a working phone. Once we left Ireland roaming rates started applying. A one minute "hi, I am here" call costs about $1. Expensive, but effective for emergencies. We went with a data plan that's 2 Euros for 50 MB that expire after 24 hours. We normally leave data disabled on the phone (to avoid paying at least 2 Euros per day), and only enable it when necessary. In the 6 weeks that we've been traveling we've only spent about 20 Euros in charges.